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Mathematics · 2025 · 5 marks
CBSE 2025 · Region 6 · Set 3 · Q33
Using integration, find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 bounded between the lines x =-a/2 to x =a/2.
Using integration, find the area of the ellipse $\displaystyle \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{y^{2}}{b^{2}}=1$ bounded between the lines $\displaystyle \mathrm{x}=-\frac{\mathrm{a}}{2}$ to $\displaystyle \mathrm{x}=\frac{\mathrm{a}}{2}$.
Marking-scheme solution
Correct Graph:
Required area $\displaystyle =\frac{4 \mathrm{~b}}{\mathrm{a}} \int_{0}^{\frac{\mathrm{a}}{2}} \sqrt{\mathrm{a}^{2}-\mathrm{x}^{2} \mathrm{dx}}$
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.