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The area between the curve x=y^2 and x=4...

The area between the curve `x=y^2` and `x=4` which divide into two equal parts by the line `x=a`. Find the value of `a`

A

`a=7^(2/3)`

B

`a=2^(2/3)`

C

`a=5^(2/3)`

D

`a=4^(2/3)`

Text Solution

Verified by Experts

area of first portion=area of second portion
`int_0^a(2sqrtx)(dx)=int_a^4(2sqrtx dx`
`2(x^(3/2)/(3/2))_0^a=2(x^(3/2)/(3/2))_a^4`
`a^(3/2)=4^(3/2)-a^(3/2)`
`2a^(3/2)=2^(2*(2/3))`
`a=4^(2/3)`
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