// Numbas version: exam_results_page_options
{"name": "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": [{"variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "metadata": {"description": "<p>5 indefinite integrals containing exponential functions</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "functions": {}, "tags": ["rebelmaths"], "variables": {"a2": {"description": "", "definition": "random(2..10 except a1 except 0)", "name": "a2", "group": "Ungrouped variables", "templateType": "anything"}, "a3": {"description": "", "definition": "random(-10..10 except 0 except 1 except -1)", "name": "a3", "group": "Ungrouped variables", "templateType": "anything"}, "a1": {"description": "", "definition": "random(2..10)", "name": "a1", "group": "Ungrouped variables", "templateType": "anything"}, "a5": {"description": "", "definition": "random(2..10)", "name": "a5", "group": "Ungrouped variables", "templateType": "anything"}, "a4": {"description": "", "definition": "random(-10..10 except 0 except 1 except -1)", "name": "a4", "group": "Ungrouped variables", "templateType": "anything"}}, "name": "Julie's copy of Integration 04: Exponential Functions", "parts": [{"prompt": "<p>Integrate $f(x)=e^{\\var{a1}x}$ with respect to $x$.&nbsp;</p>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "showCorrectAnswer": true, "answer": "1/{a1}exp({a1}x)+c", "scripts": {}, "showFeedbackIcon": true, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "type": "jme", "expectedvariablenames": [], "checkvariablenames": false}, {"prompt": "<p>Integrate $f(x)=\\var{a1}e^{\\var{a2}x}$ with respect to $x$.&nbsp;</p>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "showCorrectAnswer": true, "answer": "{a1}/{a2}exp({a2}x)+c", "scripts": {}, "showFeedbackIcon": true, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "type": "jme", "expectedvariablenames": [], "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>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "showCorrectAnswer": true, "answer": "{a3}/{a4}exp({a4}x)+{a1}/{a5}exp({a5}x)+c", "scripts": {}, "showFeedbackIcon": true, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "type": "jme", "expectedvariablenames": [], "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>", "checkingaccuracy": 0.001, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "showCorrectAnswer": true, "answer": "2/({a1}*{a5})exp({a1}x)+1/({a4}*{a3})exp({a4}x)+c", "scripts": {}, "showFeedbackIcon": true, "vsetrange": [0, 1], "vsetrangepoints": 5, "marks": 1, "checkingtype": "absdiff", "type": "jme", "expectedvariablenames": [], "checkvariablenames": false}], "variable_groups": [], "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4"], "advice": "<p>The basic results are&nbsp;</p>\n<p>$\\int(e^{x})dx=e^{x}+c$ or $\\int\\exp({x})dx=\\exp({x})+c$<br/>&nbsp; &nbsp; &nbsp;</p>\n<p>$\\int(e^{kx})dx=\\dfrac{1}{k}e^{kx}+c$ or $\\int\\exp({kx})dx=\\dfrac{1}{k}\\exp({kx})+c$<br/><strong></strong></p>\n<p><strong>Don't forget the constant!</strong></p>", "statement": "<p>The basic results are&nbsp;</p>\n<p>$\\int(e^{x})dx=e^{x}+c$ or $\\int\\exp({x})dx=\\exp({x})+c$<br/>&nbsp; &nbsp; &nbsp;</p>\n<p>$\\int(e^{kx})dx=\\dfrac{1}{k}e^{kx}+c$ or $\\int\\exp({kx})dx=\\dfrac{1}{k}\\exp({kx})+c$<br/><strong></strong></p>\n<p><strong>Don't forget the constant!</strong></p>", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}