Question

The area of the region described by `A = {(x,y) : x^2 + y^2 lt= 1and y^2 lt= 1- x}` is
A. `(pi)/(2)+(4)/(3)`
B. `(pi)/(2)-(4)/(3)`
C. `(pi)/(2)-(2)/(3)`
D. `(pi)/(2)+(2)/(3)`

Answer 1

Correct Answer - A
Given, `A={(x,y):x^(2)+y^(2) le 1 " and " y^(2) le 1- x,} `

Required area `=(1)/(2)pi r^(2)+2 int_(0)^(1)(1-y^(2))dy`
`=(1)/(2)pi(1)^(2)+2(y-(y^(3))/(3))_(0)^(1)`
`=((pi)/(2)+(4)/(3))` sq units