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← JEE Main 2022 · 29 Jul · Shift 1
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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 16

The area of the region {(x,y):∣x−1∣≤y≤5−x2}\left\{(x,y):|x-1|\le y\le\sqrt{5-x^2}\right\} is equal to :

Choose one option
Answer and worked solution

Official answer: D

Corners. ∣x−1∣=5−x2|x-1|=\sqrt{5-x^2} at x=−1x=-1 and x=2x=2.

Area ∫−125−x2 dx−∫−12∣x−1∣ dx=(2+52⋅π2)−52=5π4−12\displaystyle\int_{-1}^2\sqrt{5-x^2}\,dx-\int_{-1}^2|x-1|\,dx=\left(2+\frac52\cdot\frac\pi2\right)-\frac52=\frac{5\pi}4-\frac12 (using sin⁡−125+sin⁡−115=π2\sin^{-1}\frac2{\sqrt5}+\sin^{-1}\frac1{\sqrt5}=\frac\pi2).

(D)

Topics:Area between curves
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