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Find the area bounded by the curve x^2=4...

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

A

`7/8`

B

`3/4`

C

`9/8`

D

`5/4`

Text Solution

Verified by Experts

The correct Answer is:
C
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)
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