CBSE 2025 · Region 5 · Set 2 · Q32 · 5 marks
Draw a rough sketch of the curve $\displaystyle \mathrm{y}=\sqrt{\mathrm{x}}$. Using integration, find the area of the region bounded by the curve $\displaystyle \mathrm{y}=\sqrt{\mathrm{x}}, \mathrm{x}=4$ and $\displaystyle \mathrm{x}$-axis, in the first quadrant.
Marking-scheme solution
Required area $\displaystyle =\int_{0}^{4} \sqrt{\mathrm{x}} \mathrm{dx}$
\[\begin{aligned}
& =\frac{2}{3}\left[\mathrm{x}^{3 / 2}\right]_{0}^{4} \\
& =\frac{2}{3} \times 8=\frac{16}{3}
\end{aligned}
\]
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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.