Area enclosed between the curves $ |\mathrm{y}|=1-\mathrm{x}^{2} $ and $ \mathrm{x}^{2}+\mathrm{y}^{2}=1 $ is

Question

Area enclosed between the curves $ |\mathrm{y}|=1-\mathrm{x}^{2} $ and $ \mathrm{x}^{2}+\mathrm{y}^{2}=1 $ is, $ \frac{3 \pi-8}{3} $ sq. units, $ \frac{\pi-8}{3} $ sq. units, $ \frac{2 \pi-8}{3} $ sq. units, None of these

MARKS App · Accepted Answer

The dotted area is A = ∫ 0 1 1 - x 2 d x = x - x 3 3 0 1 = 1 - 1 3 = 2 3 Hence, area bounded by circle x 2 + y 2 = 1 and y = 1 - x 2 = L i n e d a r e a = A r e a o f c u r c l e - A r e a b o u n d e d b y y = 1 - x 2 = π - 4 . 2 3 = 3 π - 8 3 s q . u n i t s

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