// Numbas version: finer_feedback_settings
{"name": "Integration - sin(bx+a) and cos(bx+a)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"b": {"templateType": "anything", "name": "b", "description": "", "definition": "repeat(random(-5..5),2)", "group": "Ungrouped variables"}, "p1": {"templateType": "anything", "name": "p1", "description": "", "definition": "shuffle(-5..5 except 0)", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "name": "a", "description": "", "definition": "repeat(random(2..10 except 0),2) ", "group": "Ungrouped variables"}, "c1": {"templateType": "anything", "name": "c1", "description": "", "definition": "shuffle(-5..5 except 0)", "group": "Ungrouped variables"}}, "statement": "<p><strong>Find the following:</strong></p>\n<p><em>In each case, you may assume that the constant of integration is 0.</em></p>\n<p><em>Remember to put your argument in brackets!</em></p>", "name": "Integration - sin(bx+a) and cos(bx+a)", "parts": [{"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": true, "extendBaseMarkingAlgorithm": true, "customName": "", "musthave": {"showStrings": true, "message": "<p>Remember to put your argument in brackets!</p>", "strings": [")", "("], "partialCredit": 0}, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "failureRate": 1, "valuegenerators": [{"name": "x", "value": ""}], "showFeedbackIcon": true, "prompt": "<p>$\\int \\simplify{{a[0]}*cos({p1[0]}x+{b[0]})} \\mathrm{d}x$</p>", "marks": 1, "checkVariableNames": false, "answerSimplification": "all", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answer": "{a[0]}*sin({p1[0]}x+{b[0]})/{p1[0]}", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": true, "extendBaseMarkingAlgorithm": true, "customName": "", "musthave": {"showStrings": true, "message": "<p>Remember to put your argument in brackets!</p>", "strings": [")", "("], "partialCredit": 0}, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "failureRate": 1, "valuegenerators": [{"name": "x", "value": ""}], "showFeedbackIcon": true, "prompt": "<p>$\\int \\simplify{{c1[0]}x - sin({p1[1]}x+{b[1]})} \\mathrm{d}x$</p>", "marks": 1, "checkVariableNames": false, "answerSimplification": "all", "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answer": "({c1[0]}/2)*x^2+cos({p1[1]}x+{b[1]})/{p1[1]}", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "functions": {}, "rulesets": {}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "ungrouped_variables": ["p1", "a", "b", "c1"], "advice": "<p>$\\displaystyle\\int \\cos(bx+a) \\mathrm{d}x = \\frac{\\sin(bx+a)}{b}$</p>\n<p>$\\displaystyle\\int \\sin(cx+a) \\mathrm{d}x = \\frac{-\\cos(cx+a)}{c}$</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "type": "question", "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}