CBSE 2025 · Region 6 · Set 2 · Q33 · 5 marks
Use integration to find the area of the region enclosed by curve $\displaystyle \mathrm{y}=-\mathrm{x}^{2}$ and the straight lines $\displaystyle \mathrm{x}=-3, \mathrm{x}=2$ and $\displaystyle \mathrm{y}=0$. Sketch a rough figure to illustrate the bounded region.
Marking-scheme solution
Correct Graph:
\[\begin{aligned}
\text { Required area } & =\left|\int_{-3}^{2}-\mathrm{x}^{2} \mathrm{dx}\right| \\
= & \left.\left\lvert\,-\frac{1}{3} \mathrm{x}^{3}\right.\right]_{-3}^{2} \mid \\
= & \left|-\frac{1}{3}(\mathbf{8}-(-\mathbf{2 7}))\right| \\
& =\frac{35}{3}
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.