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Find the area of the region bounded by x...

Find the area of the region bounded by `x^2=16 y ,\ y=1,\ y=4` and the y-axis in the first quadrant.

Text Solution

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`x^(2)=4y` is the equation of the parabola.

The area of the region bounded by `x^(2)=4y, y=2, y=4` and Y-axis
`=` area of ABCDA
`=int_(2)^(4)xdy=int_(2)^(4)2sqrt(y)dy`
`=2*[(y^(3//2))/(3//2)]_(2)^(4)=(4)/(3)[4^(3//2)-2^(3//2)]`
`=(4)/(3)(8-2sqrt(2))` sq. units
`=(8)/(3)(4-sqrt(2))` sq. units.
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