// Numbas version: exam_results_page_options
{"name": "Integration by Parts", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Integration by Parts</p>\n<p>rebelmaths</p>"}, "tags": ["rebelmaths"], "variable_groups": [], "extensions": [], "ungrouped_variables": ["a", "b"], "name": "Integration by Parts", "rulesets": {}, "advice": "<p>Use Integration by Parts</p>", "variables": {"b": {"definition": "random(2..4 except a)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "b"}, "a": {"definition": "random(2..5)", "templateType": "anything", "group": "Ungrouped variables", "description": "", "name": "a"}}, "preamble": {"css": "", "js": ""}, "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Integration by Parts</p>", "parts": [{"minValue": "-2", "showCorrectAnswer": true, "prompt": "<p>Evaluate $\\int_0^\\pi x \\cos(x) \\mathrm{dx}$ using integration by parts, letting $u = x$ and $\\mathrm{dv} = \\cos(x)$</p>", "correctAnswerFraction": false, "showFeedbackIcon": true, "maxValue": "-2", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false}, {"showCorrectAnswer": true, "gaps": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "showFeedbackIcon": true, "vsetrange": [0, 1], "checkingtype": "absdiff", "checkvariablenames": false, "type": "jme", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "vsetrangepoints": 5, "marks": 1, "answer": "{b}^({a}+1)/({a}+1)", "showpreview": true}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "showFeedbackIcon": true, "vsetrange": [0, 1], "checkingtype": "absdiff", "checkvariablenames": false, "type": "jme", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "vsetrangepoints": 5, "marks": 1, "answer": "-{b}^({a}+1)/({a}+1)^2+1/({a}+1)^2", "showpreview": true}], "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "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>", "showFeedbackIcon": true, "type": "gapfill", "variableReplacements": []}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "showFeedbackIcon": true, "vsetrange": [0, 1], "checkingtype": "absdiff", "checkvariablenames": false, "type": "jme", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "vsetrangepoints": 5, "marks": 1, "answer": "1/2*1/pi-1/(pi)^2", "showpreview": true, "prompt": "<p>Evaluate $\\int_0^{1/2}x\\cos(x)\\mathrm{dx}$ using the substitution $u = x$ and $\\mathrm{dv} = \\cos(\\pi x)\\mathrm{dx}$.</p>\n<p>When writing $\\pi$ in your answer simly write pi.</p>"}], "type": "question", "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}