// Numbas version: exam_results_page_options {"name": " Definite Integrals 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h", "k", "j", "l"], "parts": [{"expectedvariablenames": [], "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "prompt": "

$\\int_\\var{a}^\\var{b}(1 + \\var{c}x)dx$

", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showpreview": true, "answer": "{b}+{c}{b}^2/2-{a}-{a}^2{c}/2", "type": "jme"}, {"expectedvariablenames": [], "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "prompt": "

$\\int_\\var{d}^\\var{f} (x^2 + \\var{g}x-\\var{h})dx$

", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showpreview": true, "answer": "{f}^3/3+{g}{f}^2/2-{h}{f}-{d}^3/3-{g}{d}^2/2+{h}{d}", "type": "jme"}, {"expectedvariablenames": [], "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "prompt": "

$\\int_\\var{j}^\\var{k}(x^3-\\var{l}x^2)dx$

", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showpreview": true, "answer": "{k}^4/4-{l}{k}^3/3-{j}^4/4+{l}{j}^3/3", "type": "jme"}, {"expectedvariablenames": [], "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "prompt": "

$\\int_1^4\\frac{3}{4x}dx$

", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showpreview": true, "answer": "3/4*ln(4)", "type": "jme"}, {"expectedvariablenames": [], "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "prompt": "

$\\int_0^{\\frac{\\pi}{12}}\\sin{6x}\\,dx$

", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showpreview": true, "answer": "1/6", "type": "jme"}, {"expectedvariablenames": [], "showFeedbackIcon": true, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "prompt": "

$\\int_0^2x(2x+3)dx$

", "vsetrangepoints": 5, "checkingtype": "absdiff", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showpreview": true, "answer": "34/3", "type": "jme"}], "statement": "

Evaluate the integrals:

", "name": " Definite Integrals 1", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "extensions": [], "functions": {}, "advice": "

First integrate the function and then substitute in the given limits.

", "variables": {"b": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b", "definition": "random(1..5)"}, "a": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a", "definition": "random(-4..0)"}, "h": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "h", "definition": "random(2..8)"}, "k": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "k", "definition": "random(1..4)"}, "f": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "f", "definition": "random(1..4)"}, "l": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "l", "definition": "random(2..6)"}, "d": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d", "definition": "random(-4..0)"}, "g": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "g", "definition": "random(2..6)"}, "j": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "j", "definition": "random(-4..0)"}, "c": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c", "definition": "random(2..6)"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Simple Definite Integrals

\n

\n

"}, "tags": [], "type": "question", "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}