// Numbas version: exam_results_page_options {"name": "Jo's basic indefinite integrals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "

Simple Indefinite Integrals

\n

", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "tags": [], "advice": "

Indefinite Integrals

", "variables": {"b": {"templateType": "anything", "description": "", "definition": "random(2..9 except a)", "group": "Ungrouped variables", "name": "b"}, "c": {"templateType": "anything", "description": "", "definition": "random(1..9 except a except b)", "group": "Ungrouped variables", "name": "c"}, "a": {"templateType": "anything", "description": "", "definition": "random(2..9)", "group": "Ungrouped variables", "name": "a"}, "f": {"templateType": "anything", "description": "", "definition": "random(1..8 except d)", "group": "Ungrouped variables", "name": "f"}, "d": {"templateType": "anything", "description": "", "definition": "random(1..8)", "group": "Ungrouped variables", "name": "d"}}, "variable_groups": [], "ungrouped_variables": ["a", "c", "b", "d", "f"], "extensions": [], "statement": "

Solve the following indefinite integrals, using $C$ to represent an unknown constant.

", "name": "Jo's basic indefinite integrals", "functions": {}, "parts": [{"scripts": {}, "failureRate": 1, "expectedVariableNames": [], "type": "jme", "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "marks": 1, "checkingAccuracy": 0.001, "showPreview": true, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingType": "absdiff", "customMarkingAlgorithm": "malrules:\n [\n [\"1/6x^(3/2)-6/7x^(7/2)\",\"Don't forget the constant of integration!\",0.9],\n [\"1/6x^(3/2)-2(x^5)^(3/2)+C\", \"Check the second term again. Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/6x^(3/2)-2(x^5)^(3/2)\", \"Check the second term again. Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/4x^(1/2)-2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/4x^(1/2)-2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/4x^(1/2)-9/2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/4x^(1/2)-9/2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/4x^(1/2)-6/7x^(7/2)\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\",0],\n [\"1/4x^(1/2)-6/7x^(7/2)+C\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\",0],\n [\"1/4x^(1/2)-21/2x^(7/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"1/4x^(1/2)-21/2x^(7/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"1/2x^(1/2)-2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/2x^(1/2)-2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/2x^(1/2)-9/2(x^5)^(3/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/2x^(1/2)-9/2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"1/2x^(1/2)-6/7x^(7/2)\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\",0],\n [\"1/2x^(1/2)-6/7x^(7/2)+C\", \"You need to look at the first term again. $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated.\",0],\n [\"1/2x^(1/2)-21/2x^(7/2)\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"1/2x^(1/2)-21/2x^(7/2)+C\", \"You need to look at both terms again. First term: $\\\\sqrt{x}=x^{\\\\frac{1}{2}}$ but this has not actually been integrated. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"3/8x^(3/2)-2(x^5)^(3/2)\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"3/8x^(3/2)-2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"3/8x^(3/2)-9/2(x^5)^(3/2)\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"3/8x^(3/2)-9/2(x^5)^(3/2)+C\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: Try to write the power on the $x$ as a single power rather than $(x^5)^{\\\\frac{1}{2}}$ before integrating. Remember, if the powers are side by side, multiply them: $\\\\sqrt{x^5}=(x^5)^{\\\\frac{1}{2}}=x^{5 \\\\times \\\\frac{1}{2}}=x^{\\\\frac{5}{2}}$.\",0],\n [\"3/8x^(3/2)-6/7x^(7/2)\", \"You need to look at the first term again. It looks like you have multiplied by the new power of $\\\\frac{3}{2}$.\",0],\n [\"3/8x^(3/2)-6/7x^(7/2)+C\", \"You need to look at the first term again. It looks like you have multiplied by the new power of $\\\\frac{3}{2}$.\",0],\n [\"3/8x^(3/2)-21/2x^(7/2)\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"3/8x^(3/2)-21/2x^(7/2)+C\", \"You need to look at both terms again. First term: It looks like you have multiplied by the new power of $\\\\frac{3}{2}$. Second term: It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"1/6x^(3/2)-21/2x^(7/2)\", \"You need to look at the second term again. It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0],\n [\"1/6x^(3/2)-21/2x^(7/2)+C\", \"You need to look at the second term again. It looks like you have multiplied by the new power of $\\\\frac{7}{2}$...\",0]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1],\"credit\":x[2]],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))$\\int{(\\frac{1}{4}\\sqrt{x}-3\\sqrt{x^5})}\\mathrm{dx}$

", "unitTests": [], "variableReplacements": [], "answer": "1/6x^(3/2)-6/7x^(7/2)+c"}], "type": "question", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}, {"name": "Jo-Ann Lyons", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2630/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}, {"name": "Jo-Ann Lyons", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2630/"}]}