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The area in the first quadrant between x...

The area in the first quadrant between `x^2+y^2=pi^2` and `y=sinx` is (a) `((pi^(3)-8))/(4)` (b) `(pi^(3))/(4)` (c) `((pi^(3)-16))/(4)` (d) `((pi^(3)-8))/(2)`

A

`((pi^(3)-8))/(4)`

B

`(pi^(3))/(4)`

C

`((pi^(3)-16))/(4)`

D

`((pi^(3)-8))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Graph of the function is as shown in the following figure:

From the figure bounded area A
`="(Area of quarter of circle)"-("Area bounded by y = sin x and x-axis between x = 0 and x "=pi//2)`
`=(pi(pi)^(2))/(4)-2`
`=((pi^(3)-8))/(4)`
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