Discussion Forum



1)

The area of the region described by $A= \left\{(X,Y):x^{2}+y^{2}\leq 1 \right\}    and   \left\{y^{2}\leq 1-x\right\}$ is


A) $\frac{\pi}{2}+\frac{4}{3}$

B) $\frac{\pi}{2}-\frac{4}{3}$

C) $\frac{\pi}{2}-\frac{2}{3}$

D) $\frac{\pi}{2}+\frac{2}{3}$

Answer:

Option A

Explanation:

Given,   $A= \left\{(X,Y):x^{2}+y^{2}\leq 1 \right\}    and   \left\{y^{2}\leq 1-x\right\}$ is

1932021189_c2.PNG

Required area =   $\frac{1}{2}\pi r^{2}+2\int_{0}^{1} (1-y^{2})dy$

                     =  $\frac{1}{2}\pi (1)^{2}+2\left(y-\frac{y^{3}}{3}\right)_0^1$

                           =$\frac{\pi}{2}+\frac{4}{3}$