Simple Indefinite Integrals

\n", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "preamble": {"css": "", "js": ""}, "advice": "Indefinite Integrals

", "rulesets": {}, "extensions": [], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "f"], "name": "indefinite integral 3", "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "variables": {"b": {"name": "b", "definition": "random(2..9 except a)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "a": {"name": "a", "definition": "random(2..9)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "d": {"name": "d", "definition": "random(1..8)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "f": {"name": "f", "definition": "random(1..8 except d)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "c": {"name": "c", "definition": "random(1..9 except a except b)", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "statement": "Solve the following indefinite integrals, using $C$ to represent an unknown constant.

", "parts": [{"type": "jme", "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 )))