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Mathematics · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 2 · Q7
Using integration, find the area of the region {( x, y ): y^2 ≤ x ≤ y }.
Using integration, find the area of the region $\displaystyle \left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^{2} \leq \mathrm{x} \leq \mathrm{y}\right\}$.
Marking-scheme solution
Clearly \(\displaystyle x\) coordinates of point of intersection are $\displaystyle 0$, $\displaystyle 1$
Required area \(\displaystyle =\int_{0}^{1}(\sqrt{x}-x) d x\)
\[\begin{aligned}
& =\left[\frac{2 x^{\frac{3}{2}}}{3}-\frac{x^{2}}{2}\right]_{0}^{1} \\
& =\frac{1}{6}
\end{aligned}
\]
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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.