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Find the area bounded by the curve x^(2)...

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

Text Solution

Verified by Experts

The correct Answer is:
`(9)/(8)` sq units
The point of intersection of the curves `x^(2) =4y and x=4y-2` could be sketched are `x= -1 and x=2.`
`therefore ` Required area
`=int_(-1)^(2){((x+2)/(4))-((x^(2))/(4))}dx`
`=(1)/(4) [(x^(2))/(2)+2x-(x^(3))/(3)]_(-1)^(2)`
`=(1)/(4) [(2+4-(8)/(3))-((1)/(2)-2+(1)/(3))]`
`=(1)/(4)[(10)/(3) -((-7)/(6))]=(1)/(4)*(9)/(2)=(9)/(8)` sq units
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