// Numbas version: exam_results_page_options
{"name": "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"], "functions": {}, "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>\n<p>No solutions given in Advice to parts a and c.</p>\n<p>Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.</p>"}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "ungrouped_variables": ["a", "b", "m3", "s2", "ans2", "ans3", "b2", "ans1", "tol", "b1", "w", "m2", "c1", "d1", "tans1", "tol1", "tans3", "t"], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "customMarkingAlgorithm": "", "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>", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "scripts": {}, "minValue": "ans1-tol", "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "type": "numberentry", "maxValue": "ans1+tol", "showFeedbackIcon": true, "mustBeReducedPC": 0, "mustBeReduced": false, "variableReplacements": [], "allowFractions": false}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "unitTests": []}, {"variableReplacementStrategy": "originalfirst", "marks": 0, "customMarkingAlgorithm": "", "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>", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "scripts": {}, "minValue": "ans2-tol", "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "type": "numberentry", "maxValue": "ans2+tol", "showFeedbackIcon": true, "mustBeReducedPC": 0, "mustBeReduced": false, "variableReplacements": [], "allowFractions": false}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "unitTests": []}, {"variableReplacementStrategy": "originalfirst", "marks": 0, "customMarkingAlgorithm": "", "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>", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "scripts": {}, "minValue": "ans3-tol", "notationStyles": ["plain", "en", "si-en"], "extendBaseMarkingAlgorithm": true, "type": "numberentry", "maxValue": "ans3+tol", "showFeedbackIcon": true, "mustBeReducedPC": 0, "mustBeReduced": false, "variableReplacements": [], "allowFractions": false}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "unitTests": []}], "preamble": {"css": "", "js": ""}, "variables": {"d1": {"group": "Ungrouped variables", "description": "", "definition": "random(-9..9)", "name": "d1", "templateType": "anything"}, "tans3": {"group": "Ungrouped variables", "description": "", "definition": "1/m3*((1-w)*sin(m3*pi/2)-w*(cos(m3*pi/2)-1))", "name": "tans3", "templateType": "anything"}, "tol1": {"group": "Ungrouped variables", "description": "", "definition": "0.0001", "name": "tol1", "templateType": "anything"}, "b2": {"group": "Ungrouped variables", "description": "", "definition": "random(1..20)", "name": "b2", "templateType": "anything"}, "m2": {"group": "Ungrouped variables", "description": "", "definition": "random(1..9)", "name": "m2", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "random(-2..2#0.5 except 0)", "name": "a", "templateType": "anything"}, "ans3": {"group": "Ungrouped variables", "description": "", "definition": "precround(tans3,3)", "name": "ans3", "templateType": "anything"}, "b1": {"group": "Ungrouped variables", "description": "", "definition": "random(-1..2#0.5 except 0)", "name": "b1", "templateType": "anything"}, "m3": {"group": "Ungrouped variables", "description": "", "definition": "random(2..9)", "name": "m3", "templateType": "anything"}, "w": {"group": "Ungrouped variables", "description": "", "definition": "random(0,1)", "name": "w", "templateType": "anything"}, "tol": {"group": "Ungrouped variables", "description": "", "definition": "0.001", "name": "tol", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "description": "", "definition": "random(2..5)", "name": "b", "templateType": "anything"}, "t": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "t", "templateType": "anything"}, "c1": {"group": "Ungrouped variables", "description": "", "definition": "t*random(1..9)", "name": "c1", "templateType": "anything"}, "s2": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "s2", "templateType": "anything"}, "ans1": {"group": "Ungrouped variables", "description": "", "definition": "precround(tans1,3)", "name": "ans1", "templateType": "anything"}, "ans2": {"group": "Ungrouped variables", "description": "", "definition": "precround(1/b*(ln(1+b*b2/m2)),3)", "name": "ans2", "templateType": "anything"}, "tans1": {"group": "Ungrouped variables", "description": "", "definition": "(1/a)*(e^(a*b1)-1)", "name": "tans1", "templateType": "anything"}}, "type": "question", "statement": "<p>Evaluate the following definite integrals.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "extensions": [], "name": "Integration: Definite Integration", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}