CBSE 2023 · Region 1 · Set 2 · Q33 · 5 marks
Find the area of the region $\displaystyle \left\{(x, y): x^{2}+y^{2} \leq 1 \leq x+y\right\}$, using integration.
Marking-scheme solution
Required area $\displaystyle = \int_{0}^{1} \sqrt{1-x^{2}}\,dx - \int_{0}^{1} (1-x)\,dx$\[= \left.\frac{x}{2}\sqrt{1-x^{2}} + \frac{1}{2}\sin^{-1}x\ \right|_{0}^{1} + \left.\frac{(1-x)^{2}}{2}\right|_{0}^{1} \]\[= \frac{\pi}{4} - \frac{1}{2} \]Application of IntegralsArea under Simple CurvesApplylong_answerhard
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CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.