// Numbas version: exam_results_page_options
{"name": "Integration 04: Exponential Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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>", "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>5 indefinite integrals containing exponential functions</p>\n<p>rebelmaths</p>"}, "extensions": [], "variable_groups": [], "functions": {}, "rulesets": {}, "name": "Integration 04: Exponential Functions", "tags": ["rebelmaths"], "preamble": {"js": "", "css": ""}, "parts": [{"checkingtype": "absdiff", "type": "jme", "scripts": {}, "answer": "1/{a1}exp({a1}x)+c", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "expectedvariablenames": [], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "answersimplification": "all", "vsetrange": [0, 1], "prompt": "<p>Integrate $f(x)=e^{\\var{a1}x}$ with respect to $x$.&nbsp;</p>", "marks": 1, "vsetrangepoints": 5, "checkvariablenames": false, "showpreview": true, "showCorrectAnswer": true}, {"checkingtype": "absdiff", "type": "jme", "scripts": {}, "answer": "{a1}/{a2}exp({a2}x)+c", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "expectedvariablenames": [], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "answersimplification": "all", "vsetrange": [0, 1], "prompt": "<p>Integrate $f(x)=\\var{a1}e^{\\var{a2}x}$ with respect to $x$.&nbsp;</p>", "marks": 1, "vsetrangepoints": 5, "checkvariablenames": false, "showpreview": true, "showCorrectAnswer": true}, {"checkingtype": "absdiff", "type": "jme", "scripts": {}, "answer": "{a3}/{a4}exp({a4}x)+{a1}/{a5}exp({a5}x)+c", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "expectedvariablenames": [], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "answersimplification": "all", "vsetrange": [0, 1], "prompt": "<p>Integrate $f(x)=\\var{a3}\\exp(\\var{a4}x)+\\var{a1}\\exp(\\var{a5}x)$ with respect to $x$.&nbsp;</p>", "marks": 1, "vsetrangepoints": 5, "checkvariablenames": false, "showpreview": true, "showCorrectAnswer": true}, {"checkingtype": "absdiff", "type": "jme", "scripts": {}, "answer": "2/({a1}*{a5})exp({a1}x)+1/({a4}*{a3})exp({a4}x)+c", "showFeedbackIcon": true, "checkingaccuracy": 0.001, "expectedvariablenames": [], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "answersimplification": "all", "vsetrange": [0, 1], "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>", "marks": 1, "vsetrangepoints": 5, "checkvariablenames": false, "showpreview": true, "showCorrectAnswer": true}], "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4"], "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>", "variables": {"a1": {"definition": "random(2..10)", "group": "Ungrouped variables", "name": "a1", "description": "", "templateType": "anything"}, "a2": {"definition": "random(2..10 except a1 except 0)", "group": "Ungrouped variables", "name": "a2", "description": "", "templateType": "anything"}, "a5": {"definition": "random(2..10)", "group": "Ungrouped variables", "name": "a5", "description": "", "templateType": "anything"}, "a3": {"definition": "random(-10..10 except 0 except 1 except -1)", "group": "Ungrouped variables", "name": "a3", "description": "", "templateType": "anything"}, "a4": {"definition": "random(-10..10 except 0 except 1 except -1)", "group": "Ungrouped variables", "name": "a4", "description": "", "templateType": "anything"}}, "type": "question", "contributors": [{"name": "Phu Ong", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1954/"}]}]}], "contributors": [{"name": "Phu Ong", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1954/"}]}