// Numbas version: exam_results_page_options
{"name": "Indefinite integral", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Indefinite integral", "tags": ["Calculus", "Steps", "calculus", "constant of integration", "indefinite integration", "integrals", "integrating fractional powers", "integrating powers", "integration", "standard integrals", "steps"], "advice": "\n    \n    \n    <p>Using <br/>\\[\\int \\;x^n\\;dx=\\frac{x^{n+1}}{n+1}+C\\] for any number $n \\neq -1$ we have<br/>\\[\\begin{eqnarray*}\n    \n    \\simplify[std]{Int({c}*x^{m}+{d}*x ^ ({b} / {n}),x)} &#38;=&#38;\\simplify[std]{ ({c} / {m + 1}) * x ^ {m + 1} +{d}* x ^ ({b} / {n} + 1) / ({b} / {n} + 1) + C }\\\\\n    \n    &#38;=&#38;\\simplify[std]{ ({c} / {m + 1}) * x ^ {m + 1} + ({d*n} / {b + n}) * x ^ ({b + n} / {n}) + C}\n    \n    \\end{eqnarray*}\\]</p>\n    \n    \n  ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "surdf": [{"pattern": "a/sqrt(b)", "result": "(sqrt(b)*a)/b"}]}, "parts": [{"stepspenalty": 0.0, "prompt": "\n      <p>$\\simplify[std]{f(x) = {c}x ^ {m} + {d}*x^({b}/{n})}$</p>\n        <p>$\\displaystyle \\int\\;f(x)\\,dx=\\;$[[0]]</p>\n        <p>Input all numbers as integers or fractions and not decimals. Remember to include the constant of integration $C$.</p>\n        <p>Click on Show steps to get more information. You will not lose any marks by doing so.</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Input all numbers as integers or fractions and not decimals.</p>", "showstrings": false, "strings": ["."], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [1.0, 2.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 3.0, "answer": "({c}/{m+1})x ^ {m+1} + ({d*n}/{b+n})*x^({n+b}/{n})+C", "type": "jme"}], "steps": [{"prompt": "<p>The indefinite integral of a power $x^n$ where $n\\neq -1$ is \\[\\int \\;x^n\\;dx=\\frac{x^{n+1}}{n+1}+C\\]</p>", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "\n  <p>Integrate the following function $f(x)$.</p>\n    <p><br/>Input the constant of integration as $C$.</p>\n  ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(1..5)", "name": "a"}, "c": {"definition": "s1*random(2..9)", "name": "c"}, "b": {"definition": "random(2..9)", "name": "b"}, "d": {"definition": "random(2..9)", "name": "d"}, "s1": {"definition": "random(1,-1)", "name": "s1"}, "m": {"definition": "random(3..9)", "name": "m"}, "n": {"definition": "a*b+r", "name": "n"}, "r": {"definition": "random(1..b-1)", "name": "r"}}, "metadata": {"notes": "\n    \t\t<p><strong>2/08/2012:</strong></p>\n    \t\t<p>Added tags.</p>\n    \t\t<p>Added description.</p>\n    \t\t<p>Checked calculation. OK.</p>\n    \t\t<p>Added decimal point to forbidden strings along with message to user re input of numbers.</p>\n    \t\t<p>Message about Show steps included. Also another message about including the constant of integration.</p>\n    \t\t<p>Changed checking range from 0 to 1 to 1 to 2.</p>\n    \t\t<p>Improved display.</p>\n    \t\t", "description": "<p>Find $\\displaystyle \\int ax ^ m+ bx^{c/n}\\;dx$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}