// Numbas version: exam_results_page_options
{"name": "Integration: Indefinite integral", "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"}, "r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..b-1)", "description": "", "name": "r"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "a*b+r", "description": "", "name": "n"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(2..9)", "description": "", "name": "c"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "name": "d"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "name": "a"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "name": "m"}}, "ungrouped_variables": ["a", "c", "b", "d", "s1", "m", "n", "r"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Integration: Indefinite integral", "functions": {}, "showQuestionGroupNames": false, "parts": [{"stepsPenalty": 0, "scripts": {}, "gaps": [{"answer": "({c}/{m+1})x ^ {m+1} + ({d*n}/{b+n})*x^({n+b}/{n})+C", "vsetrange": [1, 2], "checkingaccuracy": 0.001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input all numbers as integers or fractions and not decimals.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "std", "marks": 3, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n\t\t\t<p>$\\simplify[std]{f(x) = {c}x ^ {m} + {d}*x^({b}/{n})}$</p>\n\t\t\t      <p>$\\displaystyle \\int\\;f(x)\\,dx=\\;$[[0]]</p>\n\t\t\t      <p>Input all numbers as integers or fractions and not decimals. Remember to include the constant of integration $C$.</p>\n\t\t\t      <p>Click on Show steps to get more information. You will not lose any marks by doing so.</p>\n\t\t\t", "steps": [{"type": "information", "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>", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "showCorrectAnswer": true, "marks": 0}], "statement": "\n\t<p>Integrate the following function $f(x)$.</p>\n\t  <p><br/>Input the constant of integration as $C$.</p>\n\t", "tags": ["Calculus", "calculus", "checked2015", "constant of integration", "indefinite integration", "integrating fractional powers", "integrating powers", "integration", "mas1601", "MAS1601", "standard integrals", "Steps", "steps"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "surdf": [{"result": "(sqrt(b)*a)/b", "pattern": "a/sqrt(b)"}]}, "preamble": {"css": "", "js": ""}, "type": "question", "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", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find $\\displaystyle \\int ax ^ m+ bx^{c/n}\\;dx$.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n\t  \n\t  \n\t  <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\t  \n\t  \\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\t  \n\t  &#38;=&#38;\\simplify[std]{ ({c} / {m + 1}) * x ^ {m + 1} + ({d*n} / {b + n}) * x ^ ({b + n} / {n}) + C}\n\t  \n\t  \\end{eqnarray*}\\]</p>\n\t  \n\t  \n\t", "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/"}]}