Find the area bounded by the curve `x^2=4y` and the straight line `x=4y-2.`

Options

A. `7/8`
B. `3/4`
C. `9/8`
D. `5/4`

Answer

C

Explanation

Required area is the shaded region in the figure . x-co-ordinates of point P and Q can be calculated by solving
`x^2=4y` and 4y=x+2 i.e. `x^2-x-2=0 rArr x=-1,2`
So, required area = `int_(-1)^2 ((x+2)/4-x^2/4)dx=1/4 int_(-1)^2 (x+2-x^2)dx=9/8` (sq.units)