// Numbas version: exam_results_page_options
{"name": "Definite integration 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"w": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "definition": "random(0,1)"}, "ans3": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "definition": "precround(tans3,2)"}, "a1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "definition": "random(1..7)"}, "ans4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "definition": "precround(tans4,4)"}, "b4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b4", "definition": "s7*random(1,2,3)"}, "p": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "definition": "n4*b4"}, "m3": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "m3", "definition": "random(2..9)"}, "c1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "definition": "t*random(1..9)"}, "ans1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "definition": "precround(tans1,2)"}, "s2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "definition": "random(1,-1)"}, "tol": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "tol", "definition": "0.01"}, "m4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "m4", "definition": "2"}, "d1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "definition": "random(-9..9)"}, "b1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "definition": "random(2..6)"}, "b2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "b2", "definition": "random(1..20)"}, "ans2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "definition": "precround(ln(1+b2/m2),2)"}, "tol1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "tol1", "definition": "0.0001"}, "s6": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s6", "definition": "-1"}, "s7": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "s7", "definition": "1"}, "tans3": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "tans3", "definition": "if(w=0,((-1)^(m3)-1)/m3^2,-pi*(-1)^(m3)/m3)"}, "m2": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "m2", "definition": "random(1..9)"}, "n4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "definition": "s6*random(1,2,3)"}, "t": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "definition": "random(1,-1)"}, "tans1": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "tans1", "definition": "a1^2*(b1^5-1)/5+a1*c1*(b1^4-1)/2+(2*a1*d1+c1^2)*(b1^3-1)/3+c1*d1*(b1^2-1)+d1^2*(b1-1)"}, "tans4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "tans4", "definition": "(e^(p)*(p^2-2*p+2)-2)/(n4^3)"}}, "functions": {}, "statement": "<p>Evaluate the following definite integral.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "extensions": [], "ungrouped_variables": ["ans1", "ans2", "ans3", "ans4", "b4", "b1", "b2", "d1", "s2", "s7", "s6", "m4", "m3", "m2", "tol", "a1", "tans4", "c1", "tans1", "tans3", "tol1", "p", "t", "w", "n4"], "parts": [{"showCorrectAnswer": true, "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "mustBeReduced": false, "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "minValue": "ans1-tol", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "marks": 4, "mustBeReducedPC": 0, "variableReplacements": [], "correctAnswerStyle": "plain", "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "customMarkingAlgorithm": "", "maxValue": "ans1+tol"}], "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "prompt": "\n  <p>\\[I=\\int_1^{\\var{b1}}\\simplify[std]{({a1} * x ^ 2 + {c1} * x + {d1})^2}\\;dx\\]</p>\n<p>$I=\\;\\;$[[0]]</p>\n<p>Input your answer to 2 decimal places.</p>\n  \n", "sortAnswers": false, "variableReplacements": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}], "tags": [], "metadata": {"description": "<p>Evaluate $\\int_1^{\\,m}(ax ^ 2 + b x + c)^2\\;dx$, $\\int_0^{p}\\frac{1}{x+d}\\;dx,\\;\\int_0^\\pi x \\sin(qx) \\;dx$, $\\int_0^{r}x ^ {2}e^{t x}\\;dx$</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"js": "", "css": ""}, "advice": "<p>a)<br/>\\[I=\\int_1^\\var{b1}\\simplify[std]{({a1} * x ^ 2 + {c1} * x + {d1})^2}\\;dx\\] <br/>Expand the parentheses to obtain:</p>\n<p>\\[\\begin{eqnarray*}I &amp;=&amp; \\int_1^\\var{b1} \\simplify[std]{{a1 ^ 2} * x ^ 4 + {2 * a1 * c1} * x ^ 3+ {c1 ^ 2+2*a1*d1} * x ^ 2 + {2 * c1 * d1} * x+ {d1 ^ 2} }\\;dx\\\\ &amp;=&amp;\\left[\\simplify[std]{{a1 ^ 2}/5 * x ^ 5 + {2 * a1 * c1}/4 * x ^ 4+ {c1 ^ 2+2*a1*d1}/3 * x ^ 3 + {2 * c1 * d1}/2 * x^2+ {d1 ^ 2}x }\\right]_1^\\var{b1}\\\\ &amp;=&amp;\\var{tans1}\\\\ \\\\&amp;=&amp;\\var{ans1}\\mbox{ to 2 decimal places} \\end{eqnarray*} \\]</p>\n<p></p>\n<p></p>", "name": "Definite integration 1", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Jo-Ann Lyons", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2630/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Jo-Ann Lyons", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2630/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}