// Numbas version: exam_results_page_options
{"name": "Hina's copy of  Integration by substitution", "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", "s1"], "name": "Hina's copy of  Integration by substitution", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "parts": [{"stepsPenalty": 1, "prompt": "<p>\\[\\simplify[std]{Int(({2 * a} * x + {b}) / ({a} * x ^ 2 + {b} * x + {c}),x)}\\]</p>\n<p>The answer is:&nbsp;&nbsp;[[0]]</p>\n<p>Input all numbers in your answers as integers or fractions (not decimals).</p>\n<p>Do not forget to include the constant of integration as $+C$ at the end of your answer</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Do not input numbers as decimals, only as integers without the decimal point, or fractions</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "answersimplification": "std", "scripts": {}, "answer": "ln(({a} * (x ^ 2)) + ({b} * x) + {c}) + C", "marks": 3, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "steps": [{"prompt": "<p>Try the substitution $u=\\simplify[std]{{a} * (x ^ 2) + ({b} * x) + {c}}$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "statement": "<p>Integrate the following by using an appropriate substitution:</p>\n<p>You can click on Show steps to get a hint. You will lose 1 mark if you do so.</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "ceil(b^2/4a+random(1..5))", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "s1*random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}}, "metadata": {"description": "<p>Find $\\displaystyle I=\\int \\frac{2 a x +b} {a x ^ 2 + b x + c}\\;dx$ by substitution or otherwise.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Hina Ahmed", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1160/"}]}]}], "contributors": [{"name": "Hina Ahmed", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1160/"}]}