// Numbas version: finer_feedback_settings
{"name": "Integration: Definite Integration 3 Integrals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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>"}, "statement": "<p><strong>Evaluate</strong> the following definite integrals.</p>", "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>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variables": {"b2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b2", "definition": "random(1..20)"}, "t": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "t", "definition": "random(1,-1)"}, "tans3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "tans3", "definition": "1/m3*(tan(m3*pi/3))"}, "w": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "w", "definition": "random(0,1)"}, "tol": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "tol", "definition": "0.001"}, "ans2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "ans2", "definition": "precround(1/b*(ln(1+b*b2/m2)),3)"}, "tans1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "tans1", "definition": "(1/a)*(e^(a*b1)-1)"}, "m3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "m3", "definition": "random(2..9)"}, "c1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c1", "definition": "t*random(1..9)"}, "m2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "m2", "definition": "random(1..9)"}, "b": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b", "definition": "random(2..5)"}, "tol1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "tol1", "definition": "0.0001"}, "b1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b1", "definition": "random(-1..2#0.5 except 0)"}, "a": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(-1.5,-0.5,0.5,1.5)"}, "d1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d1", "definition": "random(-9..9)"}, "ans3": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "ans3", "definition": "precround(tans3,3)"}, "s2": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s2", "definition": "random(1,-1)"}, "ans1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "ans1", "definition": "precround(tans1,3)"}}, "variable_groups": [], "ungrouped_variables": ["a", "b", "m3", "s2", "ans2", "ans3", "b2", "ans1", "tol", "b1", "w", "m2", "c1", "d1", "tans1", "tol1", "tans3", "t"], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Integration: Definite Integration 3 Integrals", "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "minValue": "ans1-tol", "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "maxValue": "ans1+tol", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "mustBeReducedPC": 0, "mustBeReduced": false}, {"showCorrectAnswer": true, "checkingType": "absdiff", "variableReplacements": [], "vsetRangePoints": 5, "checkVariableNames": false, "answer": "1/{a}e^({a}x)", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "expectedVariableNames": [], "vsetRange": [0, 1], "checkingAccuracy": 0.001, "marks": 1, "type": "jme", "failureRate": 1}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "customMarkingAlgorithm": "", "scripts": {}, "prompt": "<p><strong>Integrate</strong>:&nbsp; &nbsp;\\(\\int \\simplify[std]{e^({a}x)}\\;dx\\)&nbsp; =&nbsp; &nbsp;[[1]] $+C&nbsp;$</p>\n<p></p>\n<p><strong>Evaluate:&nbsp; &nbsp; &nbsp;</strong>\\(\\int_0^{\\var{b1}}\\simplify[std]{e^({a}x)}\\;dx\\)&nbsp; =&nbsp;&nbsp;[[0]]</p>\n<p>Input your answer to 3 decimal places.</p>", "marks": 0, "type": "gapfill"}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "minValue": "ans2-tol", "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "maxValue": "ans2+tol", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "mustBeReducedPC": 0, "mustBeReduced": false}, {"showCorrectAnswer": true, "checkingType": "absdiff", "variableReplacements": [], "vsetRangePoints": 5, "checkVariableNames": false, "answer": "1/{b}ln({b}x+{m2})", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "expectedVariableNames": [], "vsetRange": [0, 1], "checkingAccuracy": 0.001, "marks": 1, "type": "jme", "failureRate": 1}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "customMarkingAlgorithm": "", "scripts": {}, "prompt": "<p><strong>Integrate</strong>:&nbsp; &nbsp;\\(\\int \\dfrac{1}{\\var{b}x+\\var{m2}}\\;dx\\)&nbsp; =&nbsp; &nbsp;[[1]] $+C&nbsp;$</p>\n<p></p>\n<p></p>\n<p><strong>Evaluate:&nbsp; &nbsp; &nbsp;</strong>\\(\\int_0^{\\var{b2}}\\dfrac{1}{\\var{b}x+\\var{m2}}\\;dx\\)&nbsp; &nbsp;=&nbsp; &nbsp;[[0]]</p>\n<p>Input your answer to 3 decimal places.</p>", "marks": 0, "type": "gapfill"}, {"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "minValue": "ans3-tol", "customMarkingAlgorithm": "", "scripts": {}, "allowFractions": false, "marks": 1, "maxValue": "ans3+tol", "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "type": "numberentry", "mustBeReducedPC": 0, "mustBeReduced": false}, {"showCorrectAnswer": true, "checkingType": "absdiff", "variableReplacements": [], "vsetRangePoints": 5, "checkVariableNames": false, "answer": "1/{m3}*tan({m3}x)", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showPreview": true, "customMarkingAlgorithm": "", "scripts": {}, "expectedVariableNames": [], "vsetRange": [0, 1], "checkingAccuracy": 0.001, "marks": 1, "type": "jme", "failureRate": 1}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "unitTests": [], "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "customMarkingAlgorithm": "", "scripts": {}, "prompt": "<p><strong>Integrate</strong>:&nbsp; &nbsp;\\(\\int \\sec^2(\\var{m3}x)\\;dx\\)&nbsp; =&nbsp; &nbsp;[[1]]&nbsp;$+C&nbsp;$</p>\n<p></p>\n<p></p>\n<p><strong>Evaluate:&nbsp; &nbsp; &nbsp;</strong>\\(\\int_0^{\\pi/3}\\sec^2(\\var{m3}x)\\;dx\\)&nbsp; =&nbsp;&nbsp;[[0]]</p>\n<p>Input your answer to 3 decimal places.</p>", "marks": 0, "type": "gapfill"}], "functions": {}, "preamble": {"css": "", "js": ""}, "tags": [], "type": "question", "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}]}]}], "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}, {"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}]}