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The area of the region bounded by the cu...

The area of the region bounded by the curve `ay^(2)=x^(3)`, the Y-axis and the lines y = a and y = 2a, is

A

`(3)/(5)a^(2)(2.2^(2//3)-1)` sq unit

B

`(2)/(5)a(2^(2//3)-1)` sq unit

C

`(3)/(5)a^(2)(2^(2//3)+1)` sq unit

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
Area BMNC `=int_(a)^(2a)xdy=int_(a)^(2a)a^(1//3)y^(2//3)dy`

`=(3a^((1)/(3)))/(5)[y^(5//3)]_(a)^(2a)=(3a^((1)/(3)))/(5)((2a)^((5)/(3))-a^((5)/(3)))`
`=(3)/(5)a^((1)/(3))a^((5)/(3))((2)^((5)/(3))-1)=(3)/(5)a^(2)(2.2^((2)/(3))-1)` sq units
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