// Numbas version: exam_results_page_options
{"name": "Indefinite integration using standard integrals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s1"}, "c3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s5*random(2..8)", "description": "", "name": "c3"}, "a2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s4*random(3..9)", "description": "", "name": "a2"}, "s5": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s5"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s2*random(2..9)", "description": "", "name": "b"}, "s3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s3"}, "b1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s3*random(2..9)", "description": "", "name": "b1"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(2..5)", "description": "", "name": "a"}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s2"}, "s4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s4"}, "a1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "name": "a1"}}, "ungrouped_variables": ["a", "b", "s3", "s2", "s1", "s5", "s4", "a1", "a2", "b1", "c3"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Indefinite integration using standard integrals", "functions": {}, "showQuestionGroupNames": false, "parts": [{"showCorrectAnswer": true, "marks": 0, "scripts": {}, "gaps": [{"answer": "({b}/{a}) * e ^({a}*x) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "answersimplification": "std", "expectedvariablenames": [], "notallowed": {"message": "<p>Enter all numbers as integers or fractions and not as decimals.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 3, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n      <p>$\\simplify[std]{f(x) = {b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3}}$</p>\n      <p>$\\displaystyle \\int\\;f(x)\\,dx=\\;$[[0]]</p>\n      <p>Enter all numbers as integers or fractions and not as decimals.</p>\n      ", "steps": [{"prompt": "<p>Note that \\[\\begin{eqnarray*} &amp;\\int&amp; \\;x^n\\;dx&amp;=&amp;\\frac{x^{n+1}}{n+1}+C,\\;\\;n \\neq -1\\\\ &amp;\\int&amp; \\;\\sin(ax)\\;dx &amp;=&amp; -\\frac{1}{a}\\cos(ax)+C\\\\ &amp;\\int&amp; \\;e^{ax}\\;dx &amp;=&amp; \\frac{1}{a}e^{ax}+C\\\\ \\end{eqnarray*}\\]</p>", "scripts": {}, "type": "information", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "stepsPenalty": 0}], "statement": "\n  <p>Integrate the following function $f(x)$.</p>\n  <p><br/>You must input the constant of integration as $C$.</p>\n  ", "tags": ["Calculus", "calculus", "checked2015", "exponential function", "functions", "indefinite integral", "indefinite integration", "integration", "integration of an exponential", "integration of an integer power", "integration of trigonometric functions", "mas1601", "MAS1601", "Steps", "steps", "trigonometric function"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n                            \t\t<p>&nbsp;<strong>20/06/2012:</strong></p>\n                            \t\t<p>Added tags.</p>\n                            \t\t<p>Tidied up display of prompt using \\displaystyle.</p>\n                            \t\t<p>Problems with display of $e^{ax}$ for $a \\lt 0$. Had brackets around the $a$. (<strong>Corrected as an issue 29/06/2012</strong>).</p>\n                            \t\t<p>Mistake in Show steps, corrected.</p>\n                            \t\t<p>Added requirement to enter numbers as fractions or integers.</p>\n                            \t\t<p>&nbsp;</p>\n                            \t\t<p><strong>3/07/2012:<br /></strong></p>\n                            \t\t<p>Added tags.</p>\n                            \t\t<p>&nbsp;</p>\n                            \t\t<p><strong>9/07/2012:</strong></p>\n                            \t\t<p>Extended ruleset std to include !noLeadingMinus so that answer is displayed in the right order.</p>\n                            \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Integrate $f(x) = ae ^ {bx} + c\\sin(dx) + px^q$. Must input $C$ as the constant of integration.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n  <p>Splitting the integral into three parts and using the information in Steps we have:&nbsp;</p>\n  <p>\\[\\begin{eqnarray*}\\simplify[std]{Int({b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3},x)}&amp;=&amp;\\simplify[std]{Int({b} * e ^ ({a}*x),x)+Int({b1} * Sin({a1}*x),x)+Int({a2} * x ^ {c3},x) }\\\\ &amp;=&amp;\\simplify[std]{({b}/{a}) * (e ^({a}*x)) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C} \\end{eqnarray*}\\]</p>\n  ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}