// Numbas version: exam_results_page_options
{"name": "Recognise and apply a standard integral - subexpressions version", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Recognise and apply a standard integral - subexpressions version", "tags": [], "metadata": {"description": "<p>This question is the one described in method 2 of the example <a href=\"https://docs.numbas.org.uk/en/latest/authoring/example-gallery/standard-integral.html\">\"Apply a standard integral\"</a> in the Numbas documentation.</p>\n<p>The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\\cos(kx)$, $\\sin(kx)$, with $k$ a randomly chosen integer.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Let $f(x) = \\simplify{{function}}$.</p>", "advice": "<p>$f(x) = \\simplify{ {function} }$.</p>\n<p>The integral of $\\var{raw_function}$ with respect to $x$ is $\\var{raw_integral}$.</p>\n<p>Here, $k = \\var{k}$, so</p>\n<p>\\[ \\int f(x) \\, \\mathrm{d}x = \\simplify{ {integral} } \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"functions": {"name": "functions", "group": "Ungrouped variables", "definition": "[\n  [\"x^k\", \"1/(k+1)*x^(k+1)\", \"k^x^(k-1)\"],\n  [\"e^(k*x)\", \"1/k * e^(k*x)\", \"k*e^(k*x)\"],\n  [\"sin(k*x)\", \"-1/k * cos(k*x)\", \"k*cos(k*x)\"],\n  [\"cos(k*x)\", \"1/k * sin(k*x)\", \"-k*sin(k*x)\"]\n]", "description": "", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(functions)", "description": "", "templateType": "anything", "can_override": false}, "function": {"name": "function", "group": "Ungrouped variables", "definition": "substitute(\n  [\"k\": k],\n  expression(scenario[0])\n)", "description": "", "templateType": "anything", "can_override": false}, "integral": {"name": "integral", "group": "Ungrouped variables", "definition": "substitute(\n  [\"k\":k],\n  expression(scenario[1])\n)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(2 .. 9#1)", "description": "<p>A randomly-chosen coefficient used in most of the functions.</p>", "templateType": "randrange", "can_override": false}, "derivative": {"name": "derivative", "group": "Ungrouped variables", "definition": "substitute(\n  [\"k\":k],\n  expression(scenario[2])\n)", "description": "", "templateType": "anything", "can_override": false}, "raw_function": {"name": "raw_function", "group": "Ungrouped variables", "definition": "expression(scenario[0])", "description": "", "templateType": "anything", "can_override": false}, "raw_integral": {"name": "raw_integral", "group": "Ungrouped variables", "definition": "expression(scenario[1])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["functions", "scenario", "k", "function", "integral", "derivative", "raw_function", "raw_integral"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is $\\int f(x) \\, \\mathrm{d}x$?</p>\n<p><em>Use $C$ for the constant of integration.</em></p>", "alternatives": [{"type": "jme", "useCustomName": true, "customName": "Forgot constant of integration", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>Did you forget to include a constant of integration?</p>", "useAlternativeFeedback": false, "answer": "{integral}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "Differentiated - with C", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>It looks like you differentiated instead of integrating.</p>", "useAlternativeFeedback": false, "answer": "{derivative} + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "Differentiated - no C", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>It looks like you differentiated instead of integrating.</p>", "useAlternativeFeedback": false, "answer": "{derivative}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "answer": "{integral} + C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}]}