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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
Given curves `x^(2)=4y and x=4y-2` intersect, when
`x^(2)=x+2`
`"or "x^(2)-x-2=0`
`"or "x=2,-1`
`rArr" "y=1,1//4`
Hence, points of intersection area `A(-1,1//4),B(2,1)`

Required area = Shaded region in the figure
`=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)[(27)/(6)]=9//8` sq. units.
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