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Quiz designed to test integration of powers of x including negative powers, surds, fractions, etc.

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You have 5 minutes left!

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You forgot the constant of integration!

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

", "metadata": {"licence": "None specified", "description": "

Positive whole powers only

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You forgot the constant of integration!

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

", "metadata": {"licence": "None specified", "description": "

Positive whole powers only

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You forgot the constant of integration!

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

", "metadata": {"licence": "None specified", "description": "

Positive whole powers only

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You forgot the constant of integration!

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

", "metadata": {"licence": "None specified", "description": "

Positive whole powers only

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You forgot the constant of integration!

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

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Positive whole powers only

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Powers including some decimals and negatives

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

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You forgot the constant of integration!

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Powers including some decimals and negatives

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

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Powers including some decimals and negatives

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

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Powers including some decimals and negatives

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

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You forgot the constant of integration!

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Powers including some decimals and negatives

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Integrate the following:

\n

\$\\int\\simplify{{a}*x^{b}+1/{c}*x^{d}+{f}*x^{g}}\\;dx\$

\n

Don't forget the constant of integration.

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Including powers of x in the denominator

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First rewrite the integral without any fractions.

\n

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

\n

Any terms without fractions can be left unchanged.

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You forgot the constant of integration!

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Now integrate.

\n

Don't forget the constant of integration.

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Integrate the following:

\n

\$\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\$

", "functions": {}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "ungrouped_variables": ["f", "a", "b", "c", "d", "g"], "preamble": {"css": "", "js": ""}, "variables": {"g": {"description": "", "definition": "random(1..5 except [b,d])", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "f": {"description": "", "definition": "random(1..10 except[b,c])", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "c": {"description": "", "definition": "random(1..10 except a)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "a": {"description": "", "definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "d": {"description": "", "definition": "random(0..3 #0.1 except [b,1])", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}}, "type": "question"}, {"name": "Integrate powers of x, 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "variable_groups": [], "metadata": {"description": "

Including powers of x in the denominator

", "licence": "None specified"}, "parts": [{"showCorrectAnswer": true, "answer": "{a}*x^{-b}+{c}*x^{-d}+{f}*x^{g}", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

First rewrite the integral without any fractions.

\n

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

\n

Any terms without fractions can be left unchanged.

", "vsetrangepoints": 5, "variableReplacements": []}, {"showCorrectAnswer": true, "musthave": {"partialCredit": 0, "strings": ["+c"], "message": "

You forgot the constant of integration!

", "showStrings": false}, "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}+c", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "vsetrangepoints": 5, "variableReplacements": []}], "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\$

", "functions": {}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "ungrouped_variables": ["f", "a", "b", "c", "d", "g"], "preamble": {"css": "", "js": ""}, "variables": {"g": {"description": "", "definition": "random(1..5 except [b,d])", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "f": {"description": "", "definition": "random(1..10 except[b,c])", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "c": {"description": "", "definition": "random(1..10 except a)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "a": {"description": "", "definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "d": {"description": "", "definition": "random(0..3 #0.1 except [b,1])", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}}, "type": "question"}, {"name": "Integrate powers of x, 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "variable_groups": [], "metadata": {"description": "

Including powers of x in the denominator

", "licence": "None specified"}, "parts": [{"showCorrectAnswer": true, "answer": "{a}*x^{-b}+{c}*x^{-d}+{f}*x^{g}", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

First rewrite the integral without any fractions.

\n

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

\n

Any terms without fractions can be left unchanged.

", "vsetrangepoints": 5, "variableReplacements": []}, {"showCorrectAnswer": true, "musthave": {"partialCredit": 0, "strings": ["+c"], "message": "

You forgot the constant of integration!

", "showStrings": false}, "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}+c", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "vsetrangepoints": 5, "variableReplacements": []}], "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\$

", "functions": {}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "ungrouped_variables": ["f", "a", "b", "c", "d", "g"], "preamble": {"css": "", "js": ""}, "variables": {"g": {"description": "", "definition": "random(1..5 except [b,d])", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "f": {"description": "", "definition": "random(1..10 except[b,c])", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "c": {"description": "", "definition": "random(1..10 except a)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "a": {"description": "", "definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "d": {"description": "", "definition": "random(0..3 #0.1 except [b,1])", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}}, "type": "question"}, {"name": "Integrate powers of x, 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "variable_groups": [], "metadata": {"description": "

Including powers of x in the denominator

", "licence": "None specified"}, "parts": [{"showCorrectAnswer": true, "answer": "{a}*x^{-b}+{c}*x^{-d}+{f}*x^{g}", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

First rewrite the integral without any fractions.

\n

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

\n

Any terms without fractions can be left unchanged.

", "vsetrangepoints": 5, "variableReplacements": []}, {"showCorrectAnswer": true, "musthave": {"partialCredit": 0, "strings": ["+c"], "message": "

You forgot the constant of integration!

", "showStrings": false}, "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}+c", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "vsetrangepoints": 5, "variableReplacements": []}], "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\$

", "functions": {}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "ungrouped_variables": ["f", "a", "b", "c", "d", "g"], "preamble": {"css": "", "js": ""}, "variables": {"g": {"description": "", "definition": "random(1..5 except [b,d])", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "f": {"description": "", "definition": "random(1..10 except[b,c])", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "c": {"description": "", "definition": "random(1..10 except a)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "a": {"description": "", "definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "d": {"description": "", "definition": "random(0..3 #0.1 except [b,1])", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}}, "type": "question"}, {"name": "Integrate powers of x, 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "variable_groups": [], "metadata": {"description": "

Including powers of x in the denominator

", "licence": "None specified"}, "parts": [{"showCorrectAnswer": true, "answer": "{a}*x^{-b}+{c}*x^{-d}+{f}*x^{g}", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

First rewrite the integral without any fractions.

\n

(Remember that $\\frac{1}{x^n}=x^{-n}$.)

\n

Any terms without fractions can be left unchanged.

", "vsetrangepoints": 5, "variableReplacements": []}, {"showCorrectAnswer": true, "musthave": {"partialCredit": 0, "strings": ["+c"], "message": "

You forgot the constant of integration!

", "showStrings": false}, "answer": "{a}/{-b+1}*x^{-b+1}+{c}/{-d+1}*x^{-d+1}+{f}/{g+1}*x^{g+1}+c", "showpreview": true, "marks": 1, "scripts": {}, "vsetrange": [0, 1], "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "showFeedbackIcon": true, "checkingaccuracy": 0.001, "type": "jme", "checkingtype": "absdiff", "checkvariablenames": false, "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "vsetrangepoints": 5, "variableReplacements": []}], "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}/x^{b}+{c}/x^{d}+{f}*x^{g}}\\;dx\$

", "functions": {}, "advice": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "ungrouped_variables": ["f", "a", "b", "c", "d", "g"], "preamble": {"css": "", "js": ""}, "variables": {"g": {"description": "", "definition": "random(1..5 except [b,d])", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "f": {"description": "", "definition": "random(1..10 except[b,c])", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "c": {"description": "", "definition": "random(1..10 except a)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "a": {"description": "", "definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "d": {"description": "", "definition": "random(0..3 #0.1 except [b,1])", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "b": {"description": "", "definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}}, "type": "question"}]}, {"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Surds", "questions": [{"name": "Integrate powers of x, 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "metadata": {"description": "

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "preamble": {"css": "", "js": ""}, "functions": {}, "variable_groups": [], "tags": [], "ungrouped_variables": ["f", "a", "c", "g"], "variables": {"a": {"definition": "random(1..10)", "name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"definition": "random(1..5)", "name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "f": {"definition": "random(1..10 except [a,c])", "name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"definition": "random(1..10 except a)", "name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}*sqrt(x)-{c}*root(x,3)+{f}*x^{g}}\\;dx\$

", "advice": "", "parts": [{"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

First rewrite the integral using powers of $x$ only.

\n

Remember that:

\n
\n
• $\\sqrt{x}=x^\\frac{1}{2}$.
• \n
• $\\sqrt[3]{x}=x^\\frac{1}{3}$.
• \n
\n

Any terms without roots can be left unchanged.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{a}*x^(1/2)-{c}*x^(1/3)+{f}*x^{g}", "checkingtype": "absdiff"}, {"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "musthave": {"message": "

You forgot the constant of integration!

", "partialCredit": 0, "showStrings": false, "strings": ["+c"]}, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{2*a}/3*x^(3/2)-{3*c}/4*x^(4/3)+{f}/{g+1}*x^{g+1}+c", "checkingtype": "absdiff"}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Integrate powers of x, 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "metadata": {"description": "

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "preamble": {"css": "", "js": ""}, "functions": {}, "variable_groups": [], "tags": [], "ungrouped_variables": ["f", "a", "c", "g"], "variables": {"a": {"definition": "random(1..10)", "name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"definition": "random(1..5)", "name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "f": {"definition": "random(1..10 except [a,c])", "name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"definition": "random(1..10 except a)", "name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}*sqrt(x)-{c}*root(x,3)+{f}*x^{g}}\\;dx\$

", "advice": "", "parts": [{"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

First rewrite the integral using powers of $x$ only.

\n

Remember that:

\n
\n
• $\\sqrt{x}=x^\\frac{1}{2}$.
• \n
• $\\sqrt[3]{x}=x^\\frac{1}{3}$.
• \n
\n

Any terms without roots can be left unchanged.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{a}*x^(1/2)-{c}*x^(1/3)+{f}*x^{g}", "checkingtype": "absdiff"}, {"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "musthave": {"message": "

You forgot the constant of integration!

", "partialCredit": 0, "showStrings": false, "strings": ["+c"]}, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{2*a}/3*x^(3/2)-{3*c}/4*x^(4/3)+{f}/{g+1}*x^{g+1}+c", "checkingtype": "absdiff"}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Integrate powers of x, 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "metadata": {"description": "

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "preamble": {"css": "", "js": ""}, "functions": {}, "variable_groups": [], "tags": [], "ungrouped_variables": ["f", "a", "c", "g"], "variables": {"a": {"definition": "random(1..10)", "name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"definition": "random(1..5)", "name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "f": {"definition": "random(1..10 except [a,c])", "name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"definition": "random(1..10 except a)", "name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}*sqrt(x)-{c}*root(x,3)+{f}*x^{g}}\\;dx\$

", "advice": "", "parts": [{"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

First rewrite the integral using powers of $x$ only.

\n

Remember that:

\n
\n
• $\\sqrt{x}=x^\\frac{1}{2}$.
• \n
• $\\sqrt[3]{x}=x^\\frac{1}{3}$.
• \n
\n

Any terms without roots can be left unchanged.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{a}*x^(1/2)-{c}*x^(1/3)+{f}*x^{g}", "checkingtype": "absdiff"}, {"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "musthave": {"message": "

You forgot the constant of integration!

", "partialCredit": 0, "showStrings": false, "strings": ["+c"]}, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{2*a}/3*x^(3/2)-{3*c}/4*x^(4/3)+{f}/{g+1}*x^{g+1}+c", "checkingtype": "absdiff"}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Integrate powers of x, 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "metadata": {"description": "

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "preamble": {"css": "", "js": ""}, "functions": {}, "variable_groups": [], "tags": [], "ungrouped_variables": ["f", "a", "c", "g"], "variables": {"a": {"definition": "random(1..10)", "name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"definition": "random(1..5)", "name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "f": {"definition": "random(1..10 except [a,c])", "name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"definition": "random(1..10 except a)", "name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}*sqrt(x)-{c}*root(x,3)+{f}*x^{g}}\\;dx\$

", "advice": "", "parts": [{"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

First rewrite the integral using powers of $x$ only.

\n

Remember that:

\n
\n
• $\\sqrt{x}=x^\\frac{1}{2}$.
• \n
• $\\sqrt[3]{x}=x^\\frac{1}{3}$.
• \n
\n

Any terms without roots can be left unchanged.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{a}*x^(1/2)-{c}*x^(1/3)+{f}*x^{g}", "checkingtype": "absdiff"}, {"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

Now integrate.

\n

Don't forget the constant of integration.

", "checkvariablenames": false, "type": "jme", "vsetrange": [0, 1], "showCorrectAnswer": true, "showFeedbackIcon": true, "musthave": {"message": "

You forgot the constant of integration!

", "partialCredit": 0, "showStrings": false, "strings": ["+c"]}, "expectedvariablenames": [], "scripts": {}, "vsetrangepoints": 5, "showpreview": true, "answer": "{2*a}/3*x^(3/2)-{3*c}/4*x^(4/3)+{f}/{g+1}*x^{g+1}+c", "checkingtype": "absdiff"}], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question"}, {"name": "Integrate powers of x, 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "metadata": {"description": "

Including square roots, cube roots and fourth roots

", "licence": "None specified"}, "preamble": {"css": "", "js": ""}, "functions": {}, "variable_groups": [], "tags": [], "ungrouped_variables": ["f", "a", "c", "g"], "variables": {"a": {"definition": "random(1..10)", "name": "a", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "g": {"definition": "random(1..5)", "name": "g", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "f": {"definition": "random(1..10 except [a,c])", "name": "f", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "c": {"definition": "random(1..10 except a)", "name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "rulesets": {}, "statement": "

Integrate the following:

\n

\$\\int\\simplify{{a}*sqrt(x)-{c}*root(x,3)+{f}*x^{g}}\\;dx\$

", "advice": "", "parts": [{"variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "marks": 1, "variableReplacements": [], "prompt": "

First rewrite the integral using powers of $x$ only.

\n

Remember that:

\n
\n
• $\\sqrt{x}=x^\\frac{1}{2}$.
• \n
• $\\sqrt[3]{x}=x^\\frac{1}{3}$.
• \n
\n

Any terms without roots can be left unchanged.

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Now integrate.

\n

Don't forget the constant of integration.

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You forgot the constant of integration!

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First rewrite the integral using powers of $x$.

\n

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Now integrate.

\n

Don't forget the constant of integration.

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You forgot the constant of integration!

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This is a challenging question designed to test all the different skills you have learned.

\n

Integrate the following:

\n

\$\\int\\simplify{{a}/({b}*x^{d})-{c}/sqrt(x)+{b}*root(x,3)/{f}+{g}*x}\\;dx\$

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Including powers of x in the denominator

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