// Numbas version: exam_results_page_options
{"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": [{"preamble": {"css": "", "js": ""}, "parts": [{"expectedvariablenames": [], "answer": "{a[0]}*sin({p1[0]}x+{b[0]})/{p1[0]}", "vsetrange": [0, 1], "type": "jme", "marks": 1, "checkingtype": "absdiff", "musthave": {"showStrings": true, "strings": [")", "("], "message": "<p>Remember to put your argument in brackets!</p>", "partialCredit": 0}, "answersimplification": "all", "showCorrectAnswer": true, "prompt": "<p>$\\int \\simplify{{a[0]}*cos({p1[0]}x+{b[0]})} \\mathrm{d}x$</p>", "showpreview": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "variableReplacements": [], "checkvariablenames": false, "checkingaccuracy": 0.001}, {"expectedvariablenames": [], "answer": "({c1[0]}/2)*x^2+cos({p1[1]}x+{b[1]})/{p1[1]}", "vsetrange": [0, 1], "type": "jme", "marks": 1, "checkingtype": "absdiff", "musthave": {"showStrings": true, "strings": [")", "("], "message": "<p>Remember to put your argument in brackets!</p>", "partialCredit": 0}, "answersimplification": "all", "showCorrectAnswer": true, "prompt": "<p>$\\int \\simplify{{c1[0]}x - sin({p1[1]}x+{b[1]})} \\mathrm{d}x$</p>", "showpreview": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "variableReplacements": [], "checkvariablenames": false, "checkingaccuracy": 0.001}], "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>", "question_groups": [{"name": "", "questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0}], "variables": {"c1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c1", "definition": "shuffle(-5..5 except 0)"}, "b": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "definition": "repeat(random(-5..5),2)"}, "a": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "definition": "repeat(random(2..10 except 0),2) "}, "p1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "p1", "definition": "shuffle(-5..5 except 0)"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Integration - sin(bx+a) and cos(bx+a)", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "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>", "tags": [], "ungrouped_variables": ["p1", "a", "b", "c1"], "functions": {}, "type": "question", "rulesets": {}, "variable_groups": [], "showQuestionGroupNames": false, "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}]}], "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}