// Numbas version: exam_results_page_options
{"name": "Musa's copy of 3 Definite Integrals - 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy of 3 Definite Integrals - 1", "tags": [], "metadata": {"description": "<p>Definite Integrals</p><p></p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Evaluate the following definite integrals, giving your answer as a fraction as necessary.</p>", "advice": "<p>To evaluate a definite integral we must first integrate the function (we do not need to include c, the constant of integration) and then substitute in the given limits.</p>\n<p></p>\n<p><strong>(a)</strong></p>\n<p>$\\int_\\var{a}^\\var{b}(1 + \\var{c}x)\\mathrm{dx} =&nbsp;\\left[x + \\var{c/2}x^2\\right]_\\var{a}^\\var{b}= [(\\var{b})+&nbsp;\\var{c/2}(\\var{b})^2]-[(\\var{a}) + \\var{c/2}(\\var{a})^2]=\\simplify{{b}+ {c/2}{b}^2-{a} - {c/2}{a}^2}$</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>$\\int_\\var{d}^\\var{f} (x^2 + \\var{g}x-\\var{h})\\mathrm{dx}=&nbsp;\\left[\\frac{x^3}{3} + \\var{g/2}x^2-\\var{h}x\\right]_\\var{d}^\\var{f}=[\\frac{(\\var{f})^3}{3} + \\var{g/2}(\\var{f})^2-\\var{h}(\\var{f})]-[\\frac{(\\var{d})^3}{3} + \\var{g/2}(\\var{d})^2-\\var{h}(\\var{d})]=\\var{f^3/3 + g/2*f^2-h*f-(d^3/3 + g/2*d^2-h*d)}$</p>", "rulesets": {}, "extensions": [], "variables": {"f": {"name": "f", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything"}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(-4..0)", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-4..0)", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-4..0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "h", "k", "j", "l"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\int_\\var{a}^\\var{b}(1 + \\var{c}x)\\mathrm{dx}$</p>", "minValue": "{b}+{c}{b}^2/2-{a}-{a}^2{c}/2", "maxValue": "{b}+{c}{b}^2/2-{a}-{a}^2{c}/2", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\int_\\var{d}^\\var{f} (x^2 + \\var{g}x-\\var{h})\\mathrm{dx}$</p>", "minValue": "{f}^3/3+{g}{f}^2/2-{h}{f}-{d}^3/3-{g}{d}^2/2+{h}{d}", "maxValue": "{f}^3/3+{g}{f}^2/2-{h}{f}-{d}^3/3-{g}{d}^2/2+{h}{d}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "TEAME UCC", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/351/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}