// Numbas version: exam_results_page_options
{"name": "even power #2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "gaps": [{"precision": "3", "mustBeReducedPC": 0, "variableReplacements": [], "minValue": "3*{m}*({b}-{a})/8-{m}*sin({2}*{k}*{b})/(4*{k})+{m}*sin({2}*{k}*{a})/(4*{k})+{m}*sin({4}*{k}*{b})/(32*{k})-{m}*sin({4}*{k}*{a})/(32*{k})", "type": "numberentry", "allowFractions": false, "correctAnswerFraction": false, "mustBeReduced": false, "precisionType": "dp", "showCorrectAnswer": true, "marks": "2", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "scripts": {}, "strictPrecision": false, "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "maxValue": "3*{m}*({b}-{a})/8-{m}*sin({2}*{k}*{b})/(4*{k})+{m}*sin({2}*{k}*{a})/(4*{k})+{m}*sin({4}*{k}*{b})/(32*{k})-{m}*sin({4}*{k}*{a})/(32*{k})"}], "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill", "marks": 0, "showCorrectAnswer": true, "prompt": "<p>\\(Answer =\\)&nbsp;[[0]]</p>"}], "functions": {}, "ungrouped_variables": ["m", "a", "b", "n", "k"], "variables": {"b": {"group": "Ungrouped variables", "definition": "random(1..1.7#0.1)", "name": "b", "templateType": "randrange", "description": ""}, "n": {"group": "Ungrouped variables", "definition": "random(2..7#1)", "name": "n", "templateType": "randrange", "description": ""}, "m": {"group": "Ungrouped variables", "definition": "random(2..9#1)", "name": "m", "templateType": "randrange", "description": ""}, "a": {"group": "Ungrouped variables", "definition": "random(0..0.6#0.1)", "name": "a", "templateType": "randrange", "description": ""}, "k": {"group": "Ungrouped variables", "definition": "random(2..10#1)", "name": "k", "templateType": "randrange", "description": ""}}, "name": "even power #2", "statement": "<p>Evaluate the following definite integral correct to three decimal places:</p>\n<p style=\"padding-left: 30px;\">\\(\\int_\\var{a}^\\var{b}\\var{m}sin^4(\\var{k}t)dt\\)</p>", "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "advice": "<p>\\(\\int_\\var{a}^\\var{b}\\var{m}sin^4(\\var{k}t)dt\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\int_\\var{a}^\\var{b}\\var{m}sin^2(\\var{k}t)sin^2(\\var{k}t)dt\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\int_\\var{a}^\\var{b}\\var{m}\\left(\\frac{1}{2}(1-cos(\\simplify{2*{k}}t))\\right)\\left(\\frac{1}{2}(1-cos(\\simplify{2*{k}}t))\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\int_\\var{a}^\\var{b}\\frac{\\var{m}}{4}\\left(1-cos(\\simplify{2*{k}}t)-cos(\\simplify{2*{k}}t)+cos^2(\\simplify{2*{k}}t)\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\int_\\var{a}^\\var{b}\\frac{\\var{m}}{4}\\left(1-2cos(\\simplify{2*{k}}t)+\\frac{1}{2}(1+cos(\\simplify{4*{k}}t))\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\int_\\var{a}^\\var{b}\\frac{\\var{m}}{4}\\left(\\frac{3}{2}-2cos(\\simplify{2*{k}}t)+\\frac{1}{2}cos(\\simplify{4*{k}}t)\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\int_\\var{a}^\\var{b}\\frac{\\simplify{3*{m}}}{8}-\\frac{\\var{m}}{2}cos(\\simplify{2*{k}}t)+\\frac{\\var{m}}{8}cos(\\simplify{4*{k}}t)\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\frac{\\simplify{3*{m}}}{8}t-\\frac{\\var{m}}{\\simplify{4*{k}}}sin(\\simplify{2*{k}}t)+\\frac{\\var{m}}{\\simplify{32*{k}}}sin(\\simplify{4*{k}}t)\\Big|_\\var{a}^\\var{b}\\)</p>\n<p style=\"padding-left: 30px;\">\\(=\\frac{\\simplify{3*{m}*{b}}}{8}-\\frac{\\var{m}}{\\simplify{4*{k}}}sin(\\simplify{2*{k}*{b}})+\\frac{\\var{m}}{\\simplify{32*{k}}}sin(\\simplify{4*{k}*{b}})-\\frac{\\simplify{3*{m}*{a}}}{8}+\\frac{\\var{m}}{\\simplify{4*{k}}}sin(\\simplify{2*{k}*{a}})-\\frac{\\var{m}}{\\simplify{32*{k}}}sin(\\simplify{4*{k}*{a}})\\)</p>\n<p></p>\n<p></p>", "tags": [], "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}