// Numbas version: exam_results_page_options
{"name": "Simon'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": [{"functions": {}, "variable_groups": [], "name": "Simon's copy of Integration: Definite Integration", "parts": [{"showCorrectAnswer": true, "marks": 0, "showFeedbackIcon": true, "unitTests": [], "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "marks": 1, "correctAnswerFraction": false, "minValue": "ans1-tol", "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "mustBeReducedPC": 0, "maxValue": "ans1+tol", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "type": "numberentry", "scripts": {}, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "type": "gapfill", "scripts": {}, "variableReplacements": [], "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>", "variableReplacementStrategy": "originalfirst"}, {"showCorrectAnswer": true, "marks": 0, "showFeedbackIcon": true, "unitTests": [], "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "marks": 1, "correctAnswerFraction": false, "minValue": "ans2-tol", "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "mustBeReduced": false, "mustBeReducedPC": 0, "maxValue": "ans2+tol", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "type": "numberentry", "scripts": {}, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "type": "gapfill", "scripts": {}, "variableReplacements": [], "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>", "variableReplacementStrategy": "originalfirst"}], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "statement": "<p>Evaluate the following definite integrals.</p>", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "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>"}, "tags": [], "ungrouped_variables": ["a", "b", "m3", "s2", "ans2", "ans3", "b2", "ans1", "tol", "b1", "w", "m2", "c1", "d1", "tans1", "tol1", "tans3", "t"], "variables": {"m3": {"templateType": "anything", "description": "", "name": "m3", "group": "Ungrouped variables", "definition": "random(2..9)"}, "d1": {"templateType": "anything", "description": "", "name": "d1", "group": "Ungrouped variables", "definition": "random(-9..9)"}, "ans1": {"templateType": "anything", "description": "", "name": "ans1", "group": "Ungrouped variables", "definition": "precround(tans1,3)"}, "b1": {"templateType": "anything", "description": "", "name": "b1", "group": "Ungrouped variables", "definition": "random(-1..2#0.5 except 0)"}, "ans3": {"templateType": "anything", "description": "", "name": "ans3", "group": "Ungrouped variables", "definition": "precround(tans3,3)"}, "m2": {"templateType": "anything", "description": "", "name": "m2", "group": "Ungrouped variables", "definition": "random(1..9)"}, "t": {"templateType": "anything", "description": "", "name": "t", "group": "Ungrouped variables", "definition": "random(1,-1)"}, "c1": {"templateType": "anything", "description": "", "name": "c1", "group": "Ungrouped variables", "definition": "t*random(1..9)"}, "s2": {"templateType": "anything", "description": "", "name": "s2", "group": "Ungrouped variables", "definition": "random(1,-1)"}, "tol1": {"templateType": "anything", "description": "", "name": "tol1", "group": "Ungrouped variables", "definition": "0.0001"}, "a": {"templateType": "anything", "description": "", "name": "a", "group": "Ungrouped variables", "definition": "random(-2..2#0.5 except 0)"}, "tans1": {"templateType": "anything", "description": "", "name": "tans1", "group": "Ungrouped variables", "definition": "(1/a)*(e^(a*b1)-1)"}, "tol": {"templateType": "anything", "description": "", "name": "tol", "group": "Ungrouped variables", "definition": "0.001"}, "tans3": {"templateType": "anything", "description": "", "name": "tans3", "group": "Ungrouped variables", "definition": "1/m3*((1-w)*sin(m3*pi/2)-w*(cos(m3*pi/2)-1))"}, "w": {"templateType": "anything", "description": "", "name": "w", "group": "Ungrouped variables", "definition": "random(0,1)"}, "b2": {"templateType": "anything", "description": "", "name": "b2", "group": "Ungrouped variables", "definition": "random(1..20)"}, "ans2": {"templateType": "anything", "description": "", "name": "ans2", "group": "Ungrouped variables", "definition": "precround(1/b*(ln(1+b*b2/m2)),3)"}, "b": {"templateType": "anything", "description": "", "name": "b", "group": "Ungrouped variables", "definition": "random(2..5)"}}, "extensions": [], "advice": "<p><strong>(a)</strong>&nbsp;</p>\n<p>$\\int_0^{\\var{b1}}\\simplify[std]{e^({a}x)}\\;dx=\\left[\\frac{e^{\\var{a}x}}{\\var{a}}\\right]_0^{\\var{b1}}=[\\frac{e^{\\var{a}(\\var{b1})}}{\\var{a}}]-[\\frac{e^{\\var{a}(0)}}{\\var{a}}]=\\var{(e^(a*b1)-1)/a}$</p>\n<p></p>\n<p><strong>(b)</strong><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>", "type": "question", "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": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "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": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}