Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.
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\nMain advice is to go through the steps given in lectures: make an estimate, establish the integral(s) required, do the calculations, check your answer.
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\nThis graph represents the function $f(x) = \\simplify{{a2}*x^2+{c2}}$.
\nUse integration to calculate the area of the shaded region. Give your answer correct to 3 decimal places.
\nA = [[0]]
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\n$\\int{f(x)dx}=$
", "answer": "{a2}/3*x^3+{c2}x+C", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "area2", "maxValue": "area2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "3", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "{plotgraph1(3,x31,x32,-6,15,a3,b3,0)}
\nThis curve has equation $y = \\simplify{x^2-{a3+b3}*x + {a3*b3}}$.
\nCalculate the total area of the shaded regions. Give your answer correct to 3 decimal places.
\nA = [[0]]
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