CBSE 2024 · Region 3 · Set 1 · Q34 · 5 marks
Using integration, find the area of the region enclosed between the circle $\displaystyle x^{2}+y^{2}=16$ and the lines $\displaystyle x=-2$ and $\displaystyle x=2$.
Marking-scheme solution
Required area $\displaystyle =4\int_{0}^{2}\sqrt{16-x^{2}}\,dx$$\displaystyle =4\left[\dfrac{x}{2}\sqrt{16-x^{2}}+8\sin^{-1}\left(\dfrac{x}{4}\right)\right]_{0}^{2}$$\displaystyle =8\sqrt{3}+\dfrac{16\pi}{3}$Application of IntegralsArea under Simple CurvesApplynumericmedium
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CBSE Class 12 Mathematics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.