// Numbas version: finer_feedback_settings
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{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": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"f": {"name": "f", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(-4..0)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-4..0)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-4..0)", "description": "", "templateType": "anything", "can_override": false}}, "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", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\int_\\var{a}^\\var{b}(1 + \\var{c}x)\\mathrm{dx}$</p>", "minValue": "{b}+{c}{b}^2/2-{a}-{a}^2{c}/2", "maxValue": "{b}+{c}{b}^2/2-{a}-{a}^2{c}/2", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}], "resources": []}]}], "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/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}]}