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Sketch the region enclosed bounded by the curve, and the ordinates and . Evaluate: . Hence find the…
(i)
Sketch the region enclosed bounded by the curve, $y = x|x|$ and the ordinates $x = -1$ and $x = 1$.
Draw: region bounded by the curve $y = x|x|$ and the ordinates $x = -1$ and $x = 1$
Must show: curve $y = x|x|$, ordinates $x = -1$ and $x = 1$, bounded region
(ii)
Evaluate: $\int_0^1 x^2 \\, dx$.
(iii)
Hence find the area bounded by the curve, $y = x|x|$ and the ordinates $x = -1$ and $x = 1$.
Answer
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From ISC 2025 Specimen Mathematics Paper 1, question 18.