// Numbas version: exam_results_page_options {"name": "CA2 (2018/19) Substitution 1 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "CA2 (2018/19) Substitution 1 (custom feedback)", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..6)", "description": ""}, "c": {"name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..9)", "description": ""}, "b": {"name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..8 except a)", "description": ""}}, "ungrouped_variables": ["c", "b", "a"], "variable_groups": [], "statement": "

Find the following indefinite integral using the letter $C$ to represent any unknown constants.

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integration by Susbtitution

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Integration by susbtitution, no hint given

", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"marks": "2", "variableReplacementStrategy": "originalfirst", "type": "jme", "vsetRangePoints": 5, "checkingType": "absdiff", "variableReplacements": [], "checkVariableNames": false, "showFeedbackIcon": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "malrules:\n [\n [\"2/3*(1+e^x)^(3/2)\", \"Almost there! Did you forget to include the integration constant?\"],\n [\"e^x+2/3*e^(3x/2)\", \"$\\\\sqrt{1+e^x} \\\\neq \\\\sqrt{1}+\\\\sqrt{e^x}$. Hint: Try substitution.\"],\n [\"e^x+2/3*e^(3x/2)+C\", \"$\\\\sqrt{1+e^x} \\\\neq \\\\sqrt{1}+\\\\sqrt{e^x}$. Hint: Try substitution.\"],\n [\"2/3*(u)^(3/2)\", \"Don't forget to fill back in for $u$. You must give your answer in terms of the original variable i.e. in terms of $x$.\"],\n [\"2/3*(u)^(3/2)+C\", \"Don't forget to fill back in for $u$. You must give your answer in terms of the original variable i.e. in terms of $x$.\"],\n [\"3/2*(1+e^x)^(3/2)\", \"You have multiplied by the new power rather than dividing by it.\"],\n [\"3/2*(1+e^x)^(3/2)+C\", \"You have multiplied by the new power rather than dividing by it.\"],\n [\"3/2*u^(3/2)+C\", \"You have multiplied by the new power rather than dividing by it.\"],\n [\"3/2*u^(3/2)\", \"You have multiplied by the new power rather than dividing by it.\"],\n [\"e^x*sqrt(x+e^x)+C\",\"You cannot simply integrate individual terms that are multiplied together. Hint: Try substitution.\"],\n [\"e^x*sqrt(x+e^x)\",\"You cannot simply integrate individual terms that are multiplied together. Hint: Try substitution.\"],\n [\"u^(1/2)+C\",\"You have not actually integrated anything. You simply substituted for $1+e^x$.\"],\n [\"u^(1/2)\",\"You have not actually integrated anything. You simply substituted for $1+e^x$.\"],\n [\"(1+e^x)^(1/2)+C\",\"You have not actually integrated anything. You simply substituted for $1+e^x$ and then subbed back in again.\"],\n [\"(1+e^x)^(1/2)\",\"You have not actually integrated anything. You simply substituted for $1+e^x$ and then subbed back in again.\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\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 )))$\\int e^x \\sqrt{1+e^x} \\ dx$

", "vsetRange": [0, 1]}], "functions": {}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}