The area in the first quadrant between x^2 + y^2 = ^2 and y = x i… - Vidyadip

MCQ

The area in the first quadrant between ${x^2} + {y^2} = {\pi ^2}$ and $y = \sin x$ is

✓
$\frac{{({\pi ^3} - 8)}}{4}$
B
$\frac{{{\pi ^3}}}{4}$
C
$\frac{{({\pi ^3} - 16)}}{4}$
D
$\frac{{({\pi ^3} - 8)}}{2}$

✓

Answer

Correct option: A.

$\frac{{({\pi ^3} - 8)}}{4}$

a
(a) Area of the circle in first quadrant is $\frac{{\pi ({\pi ^2})}}{4}$

$i.e.,$ $\frac{{{\pi ^3}}}{4}$.

Also area bounded by curve $y = \sin x$ and $x -$ axis is $2$ sq. unit.

Hence required area is $\frac{{{\pi ^3}}}{4} - 2 = \frac{{{\pi ^3} - 8}}{4}$.

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