// Numbas version: exam_results_page_options {"name": "Morten's copy of Integration: Definite Integration", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": ["Calculus", "calculus", "checked2015", "definite integration", "integration", "integration by parts", "integration by parts twice", "MAS1601", "mas1601"], "metadata": {"notes": "\n \t\t
3/07/1012:
\n \t\tAdded tags.
\n \t\tChecked calculations.
\n \t\tLeft tolerances in, as easy to make minor errors in calculations.
\n \t\tImproved display in Advice.
\n \t\tSome superscripts e.g. the form a^\\var{b} in latex have to be written as a^{\\var{b}} as not displayed properly (if b has a second digit it slips down). Corrected.
\n \t\t20/07/2012:
\n \t\tSet new tolerace variables, tol=0.01, tol1=0.0001.
\n \t\tCan have expressions in Advice of the form $1\\times E$ where E is an expression. This can be remedied by rewriting - but later as not crucial.
\n \t\tAdded description.
\n \t\t \n \t\t25/07/2012:
\n \t\t\n \t\t
Added tags.
\n \t\tA lot of work in this question - Perhaps it would be more managable broken down into two separate questions?
\n \t\t\n \t\t
Question appears to be working correctly.
\n \t\t\n \t\t
\n \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "
Evaluate $\\int_0^{\\,m}e^{ax}\\;dx$, $\\int_0^{p}\\frac{1}{bx+d}\\;dx,\\;\\int_0^{\\pi/2} \\sin(qx) \\;dx$.
"}, "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Morten's copy of Integration: Definite Integration", "statement": "Evaluate the following definite integrals.
", "ungrouped_variables": ["a", "b", "m3", "s2", "ans2", "ans3", "b2", "ans1", "tol", "b1", "w", "m2", "c1", "d1", "tans1", "tol1", "tans3", "t"], "functions": {}, "advice": "\n
b)
\\[\\begin{eqnarray*}I&=&\\int_0^{\\var{b2}}\\simplify[std]{1/({b}*x+{m2})}\\;dx\\\\ &=&\\frac{1}{\\var{b}}\\left[\\ln(\\var{b}x+\\var{m2})\\right]_0^{\\var{b2}}\\\\ &=&\\frac{1}{\\var{b}}\\left\\{ \\ln(\\var{b2*b+m2})-\\ln(\\var{m2})\\right\\}\\\\ &=&\\frac{1}{\\var{b}}\\ln\\left(\\frac{\\var{b2*b+m2}}{\\var{m2}}\\right)\\\\ &=&\\var{ans2}\\mbox{ to 3 decimal places} \\end{eqnarray*} \\]
", "showQuestionGroupNames": false, "variables": {"b": {"group": "Ungrouped variables", "definition": "random(2..5)", "templateType": "anything", "name": "b", "description": ""}, "s2": {"group": "Ungrouped variables", "definition": "random(1,-1)", "templateType": "anything", "name": "s2", "description": ""}, "tol": {"group": "Ungrouped variables", "definition": "0.001", "templateType": "anything", "name": "tol", "description": ""}, "tol1": {"group": "Ungrouped variables", "definition": "0.0001", "templateType": "anything", "name": "tol1", "description": ""}, "d1": {"group": "Ungrouped variables", "definition": "random(-9..9)", "templateType": "anything", "name": "d1", "description": ""}, "m3": {"group": "Ungrouped variables", "definition": "random(2..9)", "templateType": "anything", "name": "m3", "description": ""}, "ans1": {"group": "Ungrouped variables", "definition": "precround(tans1,3)", "templateType": "anything", "name": "ans1", "description": ""}, "c1": {"group": "Ungrouped variables", "definition": "t*random(1..9)", "templateType": "anything", "name": "c1", "description": ""}, "t": {"group": "Ungrouped variables", "definition": "random(1,-1)", "templateType": "anything", "name": "t", "description": ""}, "tans1": {"group": "Ungrouped variables", "definition": "(1/a)*(e^(a*b1)-1)", "templateType": "anything", "name": "tans1", "description": ""}, "ans3": {"group": "Ungrouped variables", "definition": "precround(tans3,3)", "templateType": "anything", "name": "ans3", "description": ""}, "b1": {"group": "Ungrouped variables", "definition": "random(-1..2#0.5 except 0)", "templateType": "anything", "name": "b1", "description": ""}, "m2": {"group": "Ungrouped variables", "definition": "random(1..9)", "templateType": "anything", "name": "m2", "description": ""}, "b2": {"group": "Ungrouped variables", "definition": "random(1..20)", "templateType": "anything", "name": "b2", "description": ""}, "a": {"group": "Ungrouped variables", "definition": "random(-2..2#0.5 except 0)", "templateType": "anything", "name": "a", "description": ""}, "w": {"group": "Ungrouped variables", "definition": "random(0,1)", "templateType": "anything", "name": "w", "description": ""}, "tans3": {"group": "Ungrouped variables", "definition": "1/m3*((1-w)*sin(m3*pi/2)-w*(cos(m3*pi/2)-1))", "templateType": "anything", "name": "tans3", "description": ""}, "ans2": {"group": "Ungrouped variables", "definition": "precround(1/b*(ln(1+b*b2/m2)),3)", "templateType": "anything", "name": "ans2", "description": ""}}, "question_groups": [{"pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [], "name": ""}], "type": "question", "preamble": {"js": "", "css": ""}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"gaps": [{"allowFractions": false, "showPrecisionHint": false, "scripts": {}, "minValue": "ans1-tol", "marks": 1, "maxValue": "ans1+tol", "type": "numberentry", "showCorrectAnswer": true, "correctAnswerFraction": false}], "scripts": {}, "prompt": "
\\[I=\\int_0^{\\var{b1}}\\simplify[std]{e^({a}x)}\\;dx\\]
\n$I=\\;\\;$[[0]]
\nInput your answer to 3 decimal places.
", "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"gaps": [{"allowFractions": false, "showPrecisionHint": false, "scripts": {}, "minValue": "ans2-tol", "marks": 1, "maxValue": "ans2+tol", "type": "numberentry", "showCorrectAnswer": true, "correctAnswerFraction": false}], "scripts": {}, "prompt": "\\[I=\\int_0^{\\var{b2}}\\simplify[std]{1/({b}x+{m2})}\\;dx\\]
\n$I=\\;\\;$[[0]]
\nInput your answer to 3 decimal places.
", "marks": 0, "type": "gapfill", "showCorrectAnswer": true}, {"gaps": [{"allowFractions": false, "showPrecisionHint": false, "scripts": {}, "minValue": "ans3-tol", "marks": 1, "maxValue": "ans3+tol", "type": "numberentry", "showCorrectAnswer": true, "correctAnswerFraction": false}], "scripts": {}, "prompt": "\\[I=\\int_0^{\\pi/2}\\simplify[std]{({w} * Sin({m3} * x) + {1 -w} * Cos({m3} * x))}\\;dx\\]
\n$I=\\;\\;$[[0]]
\nInput your answer to 3 decimal places.
", "marks": 0, "type": "gapfill", "showCorrectAnswer": true}], "variable_groups": [], "contributors": [{"name": "Morten Brekke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/478/"}]}]}], "contributors": [{"name": "Morten Brekke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/478/"}]}