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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 1 · Q7
Find the area of the region {( x, y ): x^2 ≤ y ≤ x +2}, using integration.
Find the area of the region $\displaystyle \left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}^{2} \leq \mathrm{y} \leq \mathrm{x}+2\right\}$, using integration.
Marking-scheme solution
(for correct figure)
\(\displaystyle x\)-coordinates of points of intersection are -$\displaystyle 1$, 2.
\[\begin{aligned}
\text { Required area } & =\int_{-1}^{2}\left[(x+2)-x^{2}\right] d x \\
& =\frac{(x+2)^{2}}{2}-\left.\frac{x^{3}}{3}\right|_{-1} ^{2} \\
& \quad=\frac{16}{3}-\frac{5}{6}=\frac{9}{2}
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.