The area (in sq. units) of the region `{(x,y):xge0,x+yle3,x^(2) le4y} and {yle1+sqrt(x)}` is

Options

A. `59/12`
B. `3/2`
C. `7/3`
D. `5/2`

Answer

d

Explanation

Let A be the area of the shaded region. Then,

`A=underset(0)overset(1)int (y_(2)-y_(1))dx + underset(1)overset(2)(y_(4)-y_(3))dx`
`implies A=underset(0)overset(1)int (1+sqrt(x) -(x^(2))/(4))dx + underset(1)overset(2)int (3-x-(x^(2))/(4))dx`
`implies A =[x+(2)/(3)x^(3//2)-(x^(3))/(12)]_(0)^(1)+[3x-(x^(2))/(2)-(x^(3))/(12)]_(1)^(2)`
`A=(19)/(12)+(10)/(3)-(29)/(12) =(5)/(2)`