// Numbas version: exam_results_page_options
{"name": "Maria's copy of Simon's copy of Julie's copy of Integration 04: Exponential Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "parts": [{"answer": "1/{a1}exp({a1}x)+c", "type": "jme", "customMarkingAlgorithm": "", "vsetRange": [0, 1], "showPreview": true, "showFeedbackIcon": true, "checkVariableNames": false, "prompt": "<p>Integrate $f(x)=e^{\\var{a1}x}$ with respect to $x$.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "scripts": {}, "answerSimplification": "all", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "failureRate": 1, "marks": 1, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": [], "checkingType": "absdiff", "vsetRangePoints": 5}, {"answer": "{a1}/{a2}exp({a2}x)+c", "type": "jme", "customMarkingAlgorithm": "", "vsetRange": [0, 1], "showPreview": true, "showFeedbackIcon": true, "checkVariableNames": false, "prompt": "<p>Integrate $f(x)=\\var{a1}e^{\\var{a2}x}$ with respect to $x$.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "scripts": {}, "answerSimplification": "all", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "failureRate": 1, "marks": 1, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": [], "checkingType": "absdiff", "vsetRangePoints": 5}, {"answer": "{a3}/{a4}exp({a4}x)+{a1}/{a5}exp({a5}x)+c", "type": "jme", "customMarkingAlgorithm": "", "vsetRange": [0, 1], "showPreview": true, "showFeedbackIcon": true, "checkVariableNames": false, "prompt": "<p>Integrate $f(x)=\\var{a3}\\exp(\\var{a4}x)+\\var{a1}\\exp(\\var{a5}x)$ with respect to $x$.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "scripts": {}, "answerSimplification": "all", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "failureRate": 1, "marks": 1, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": [], "checkingType": "absdiff", "vsetRangePoints": 5}, {"answer": "2/({a1}*{a5})exp({a1}x)+1/({a4}*{a3})exp({a4}x)+c", "type": "jme", "customMarkingAlgorithm": "", "vsetRange": [0, 1], "showPreview": true, "showFeedbackIcon": true, "checkVariableNames": false, "prompt": "<p>Integrate $f(x)=\\dfrac{2}{\\var{a5}}\\exp(\\var{a1}x)+\\dfrac{1}{\\var{a3}}\\exp(\\var{a4}x)$ with respect to $x$.&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "scripts": {}, "answerSimplification": "all", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "failureRate": 1, "marks": 1, "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": [], "checkingType": "absdiff", "vsetRangePoints": 5}], "extensions": [], "tags": [], "statement": "<p>The basic results are&nbsp;</p>\n<p>$\\int(e^{x})dx=e^{x}+c$&nbsp;<br/>&nbsp; &nbsp; &nbsp;</p>\n<p>$\\int(e^{kx})dx=\\dfrac{1}{k}e^{kx}+c$</p>\n<p></p>\n<p>Don't forget the constant&nbsp;c in your answers!</p>", "name": "Maria's copy of Simon's copy of Julie's copy of Integration 04: Exponential Functions", "advice": "<p>The answers should all follow directly from the standard result&nbsp;$\\int(e^{kx})dx=\\dfrac{1}{k}e^{kx}+c$</p>\n<p>For example<br/><br/></p>\n<p><strong>(d)</strong></p>\n<p>$\\int \\dfrac{2}{\\var{a5}}e^{\\var{a1}x}+\\dfrac{1}{\\var{a3}}e^{\\var{a4}x} \\; dx=\\dfrac{2}{\\var{a5}}\\dfrac{e^{\\var{a1}x}}{\\var{a1}}+\\dfrac{1}{\\var{a3}}\\dfrac{e^{\\var{a4}x}}{\\var{a4}}+c=\\simplify{2e^({a1}x)/({a1*a5})+e^({a4}x)/({a3*a4})+c}$&nbsp;</p>", "variable_groups": [], "preamble": {"css": "", "js": ""}, "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>5 indefinite integrals containing exponential functions</p>\n<p>rebelmaths</p>"}, "variables": {"a2": {"name": "a2", "definition": "random(2..10 except a1 except 0)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "a3": {"name": "a3", "definition": "random(-10..10 except 0 except 1 except -1)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "a5": {"name": "a5", "definition": "random(3..10)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "a4": {"name": "a4", "definition": "random(-10..10 except 0 except 1 except -1)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}, "a1": {"name": "a1", "definition": "random(2..10)", "templateType": "anything", "description": "", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4"], "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}