// Numbas version: exam_results_page_options
{"name": "MA1002 Integration by Parts", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"a": {"name": "a", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": ""}, "b": {"name": "b", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..4 except a)", "description": ""}}, "name": "MA1002 Integration by Parts", "variable_groups": [], "ungrouped_variables": ["a", "b"], "rulesets": {}, "advice": "<p>Use Integration by Parts</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"minValue": "-2", "marks": "5", "correctAnswerStyle": "plain", "allowFractions": false, "correctAnswerFraction": false, "showCorrectAnswer": false, "prompt": "<p>Evaluate $\\int_0^\\pi x \\cos(x) \\mathrm{dx}$ using integration by parts, letting $u = x$ and $\\mathrm{dv} = \\cos(x)$</p>", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "-2", "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "showFeedbackIcon": true, "variableReplacements": []}, {"prompt": "<p>Evaluate $\\int_1^\\var{b}x^\\var{a}\\ln(x)\\mathrm{dx}$ using integration by parts, letting $u = \\ln(x)$ and $\\mathrm{dv} = x^\\var{a}$.</p>\n<p>Answer: [[0]]ln({b})+[[1]]</p>\n<p></p>", "marks": 0, "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"answer": "{b}^({a}+1)/({a}+1)", "marks": "2", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "checkingtype": "absdiff", "showCorrectAnswer": false, "checkingaccuracy": 0.001, "scripts": {}, "type": "jme", "showpreview": true, "expectedvariablenames": [], "vsetrangepoints": 5, "showFeedbackIcon": true, "variableReplacements": []}, {"answer": "-{b}^({a}+1)/({a}+1)^2+1/({a}+1)^2", "marks": "2", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "checkingtype": "absdiff", "showCorrectAnswer": false, "checkingaccuracy": 0.001, "scripts": {}, "type": "jme", "showpreview": true, "expectedvariablenames": [], "vsetrangepoints": 5, "showFeedbackIcon": false, "variableReplacements": []}], "showCorrectAnswer": true, "variableReplacements": [], "showFeedbackIcon": true}, {"answer": "1/2*1/pi-1/(pi)^2", "marks": "5", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "checkingtype": "absdiff", "showCorrectAnswer": false, "prompt": "<p>Evaluate $\\int_0^{1/2}x\\cos(\\pi x)\\mathrm{dx}$ using the substitution $u = x$ and $\\mathrm{dv} = \\cos(\\pi x)\\mathrm{dx}$.</p>\n<p>When writing $\\pi$ in your answer simply write pi.</p>", "checkingaccuracy": 0.001, "scripts": {}, "type": "jme", "showpreview": true, "expectedvariablenames": [], "vsetrangepoints": 5, "showFeedbackIcon": true, "variableReplacements": []}], "preamble": {"js": "", "css": ""}, "tags": [], "statement": "<p>Integration by Parts</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Integration by Parts</p>\n<p>rebelmaths</p>"}, "extensions": [], "functions": {}, "type": "question", "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}]}]}], "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}]}