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The volume of solid generated by revolvi...

The volume of solid generated by revolving about the y-axis the figure bounded by the parabola `y=x^(2)andx=y^(2)` is

A

`(21)/(5)pi`

B

`(24)/(5)pi`

C

`(2)/(15)pi`

D

`(5)/(24)pi`

Text Solution

Verified by Experts

The correct Answer is:
C
`V= int _(0)^(1) pi x^(2)dy`

`=|pi int _(0)^(1) (y^(4)-y)dy|`
`=| pi [(y^(5))/(5)-(y^(2))/(2)]_(0)^(1)|`
`=| pi [(1)/(5)-(1)/(3)]|`
`=|(-2pi)/(15)|=(2pi)/(15)`
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