// Numbas version: exam_results_page_options
{"name": "Question 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "s1", "m", "n", "r"], "name": "Question 2", "tags": ["Calculus", "calculus", "constant of integration", "indefinite integration", "integrals", "integrating fractional powers", "integrating powers", "integration", "rebelmaths", "standard integrals", "Steps", "steps"], "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  \n\t", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "surdf": [{"pattern": "a/sqrt(b)", "result": "(sqrt(b)*a)/b"}]}, "parts": [{"stepsPenalty": 0, "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      \n\t\t\t", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Input all numbers as integers or fractions and not decimals.</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({c}/{m+1})x ^ {m+1} + ({d*n}/{b+n})*x^({n+b}/{n})+C", "marks": 3, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [1, 2]}], "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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "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  \n\t", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "s1*random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "m": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "n": {"definition": "a*b+r", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "r": {"definition": "random(1..b-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}}, "metadata": {"description": "<p></p>\n<p>indefinite integration</p>\n<p>Find $\\displaystyle \\int ax ^ m+ bx^{c/n}\\;dx$.</p>\n<p>rebel</p>\n<p>rebelmaths</p>\n<p></p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}]}