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The area (in square units) bounded by th...

The area (in square units) bounded by the curve `y^(2)=8xand x^(2)=8y,` is

A

64 sq units

B

`(64)/(3)` sq units

C

`(8)/(3)` sq units

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given, curves are `y^(2)=8x`.
`implies y = sqrt(8x)`
and `x^(2)=8y`
`implies y=(x^(2))/(8)`

The point of intersection of two curves are (0, 0), (8, 8). Now, required area
`=int_(0)^(8)(sqrt(8x)-(x^(2))/(8))dx=[(sqrt(8)x^(3//2))/(3//2)-(x^(3))/(8.3)]_(0)^(8)`
`(4sqrt(2))/(3)(8)^(3//2)-(1)/(24)(8)^(3)=(128)/(3)-(64)/(3)=(64)/(3)` sq units
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