// Numbas version: exam_results_page_options
{"name": "Nick'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": [{"parts": [{"prompt": "<p>\\[I=\\int_0^{\\var{b1}}\\simplify[std]{e^({a}x)}\\;dx\\]</p>\n      <p>$I=\\;\\;$[[0]]</p>\n      <p>Input your answer to 3 decimal places.</p>", "scripts": {}, "showCorrectAnswer": true, "marks": 0, "gaps": [{"scripts": {}, "showCorrectAnswer": true, "marks": 1, "allowFractions": false, "minValue": "ans1-tol", "correctAnswerFraction": false, "maxValue": "ans1+tol", "showPrecisionHint": false, "type": "numberentry"}], "type": "gapfill"}, {"prompt": "<p>\\[I=\\int_0^{\\var{b2}}\\simplify[std]{1/({b}x+{m2})}\\;dx\\]</p>\n        <p>$I=\\;\\;$[[0]]</p>\n        <p>Input your answer to 3 decimal places.</p>", "scripts": {}, "showCorrectAnswer": true, "marks": 0, "gaps": [{"scripts": {}, "showCorrectAnswer": true, "marks": 1, "allowFractions": false, "minValue": "ans2-tol", "correctAnswerFraction": false, "maxValue": "ans2+tol", "showPrecisionHint": false, "type": "numberentry"}], "type": "gapfill"}, {"prompt": "<p>\\[I=\\int_0^{\\pi/2}\\simplify[std]{({w} * Sin({m3} * x) + {1 -w} * Cos({m3} * x))}\\;dx\\]</p>\n      <p>$I=\\;\\;$[[0]]</p>\n      <p>Input your answer to 3 decimal places.</p>", "scripts": {}, "showCorrectAnswer": true, "marks": 0, "gaps": [{"scripts": {}, "showCorrectAnswer": true, "marks": 1, "allowFractions": false, "minValue": "ans3-tol", "correctAnswerFraction": false, "maxValue": "ans3+tol", "showPrecisionHint": false, "type": "numberentry"}], "type": "gapfill"}], "type": "question", "advice": "<p>&nbsp;</p>\n  <p>b)<br/>\\[\\begin{eqnarray*}I&amp;=&amp;\\int_0^{\\var{b2}}\\simplify[std]{1/({b}*x+{m2})}\\;dx\\\\ &amp;=&amp;\\frac{1}{\\var{b}}\\left[\\ln(\\var{b}x+\\var{m2})\\right]_0^{\\var{b2}}\\\\ &amp;=&amp;\\frac{1}{\\var{b}}\\left\\{ \\ln(\\var{b2*b+m2})-\\ln(\\var{m2})\\right\\}\\\\ &amp;=&amp;\\frac{1}{\\var{b}}\\ln\\left(\\frac{\\var{b2*b+m2}}{\\var{m2}}\\right)\\\\ &amp;=&amp;\\var{ans2}\\mbox{ to 3 decimal places} \\end{eqnarray*} \\]</p>\n  <p>&nbsp;</p>", "functions": {}, "variable_groups": [], "variables": {"b1": {"definition": "random(-1..2#0.5 except 0)", "name": "b1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "tans1": {"definition": "(1/a)*(e^(a*b1)-1)", "name": "tans1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "tol": {"definition": "0.001", "name": "tol", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "m3": {"definition": "random(2..9)", "name": "m3", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "ans1": {"definition": "precround(tans1,3)", "name": "ans1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "b": {"definition": "random(2..5)", "name": "b", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "tol1": {"definition": "0.0001", "name": "tol1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "t": {"definition": "random(1,-1)", "name": "t", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "a": {"definition": "random(-2..2#0.5 except 0)", "name": "a", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "ans2": {"definition": "precround(1/b*(ln(1+b*b2/m2)),3)", "name": "ans2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "w": {"definition": "random(0,1)", "name": "w", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c1": {"definition": "t*random(1..9)", "name": "c1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "ans3": {"definition": "precround(tans3,3)", "name": "ans3", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "d1": {"definition": "random(-9..9)", "name": "d1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "s2": {"definition": "random(1,-1)", "name": "s2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "b2": {"definition": "random(1..20)", "name": "b2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "tans3": {"definition": "1/m3*((1-w)*sin(m3*pi/2)-w*(cos(m3*pi/2)-1))", "name": "tans3", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "m2": {"definition": "random(1..9)", "name": "m2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": [], "name": ""}], "preamble": {"css": "", "js": ""}, "name": "Nick's copy of Integration: Definite Integration", "tags": ["Calculus", "calculus", "checked2015", "definite integration", "integration", "integration by parts", "integration by parts twice", "MAS1601", "mas1601"], "statement": "<p>Evaluate the following definite integrals.</p>", "metadata": {"description": "<p>Evaluate $\\int_0^{\\,m}e^{ax}\\;dx$, $\\int_0^{p}\\frac{1}{bx+d}\\;dx,\\;\\int_0^{\\pi/2} \\sin(qx) \\;dx$.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International", "notes": "\n                        \t\t<p><strong>3/07/1012:</strong></p>\n                        \t\t        <p>Added tags.</p>\n                        \t\t        <p>Checked calculations.</p>\n                        \t\t        <p>Left tolerances in, as easy to make minor errors in calculations.</p>\n                        \t\t        <p>Improved display in Advice.</p>\n                        \t\t        <p>Some 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.</p>\n                        \t\t        <p><strong>20/07/2012:</strong></p>\n                        \t\t        <p>Set new tolerace variables, tol=0.01, tol1=0.0001.</p>\n                        \t\t        <p>Can 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.</p>\n                        \t\t        <p>Added description.</p>\n                        \t\t        <p></p>\n                        \t\t        <p><strong>25/07/2012:</strong></p>\n                        \t\t        <p>&nbsp;</p>\n                        \t\t        <p>Added tags.</p>\n                        \t\t        <p>A lot of work in this question - Perhaps it would be more managable broken down into two separate questions?</p>\n                        \t\t        <p>&nbsp;</p>\n                        \t\t        <p>Question appears to be working correctly.</p>\n                        \t\t        <p>&nbsp;</p>\n                        \t\t        <p>&nbsp;</p>\n                        \t\t"}, "ungrouped_variables": ["a", "b", "m3", "s2", "ans2", "ans3", "b2", "ans1", "tol", "b1", "w", "m2", "c1", "d1", "tans1", "tol1", "tans3", "t"], "showQuestionGroupNames": false, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variablesTest": {"condition": "", "maxRuns": 100}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}]}]}], "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}]}