JEE PYQ: Area Under Curves Question 17
Question 17 - 2020 (07 Jan Shift 1)
The area of the region, enclosed by the circle $x^2 + y^2 = 2$ which is not common to the region bounded by the parabola $y^2 = x$ and the straight line $y = x$, is:
(1) $\frac{1}{6}(24\pi - 1)$
(2) $\frac{1}{3}(6\pi - 1)$
(3) $\frac{1}{3}(12\pi - 1)$
(4) $\frac{1}{6}(12\pi - 1)$
Show Answer
Answer: (4) $\frac{1}{6}(12\pi - 1)$
Solution
$2\pi - \int_0^1 (\sqrt{x} - x),dx = 2\pi - \frac{1}{6} = \frac{12\pi - 1}{6}$.
BETA
