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The area enclosed between the curve y = ...

The area enclosed between the curve `y = 1 + x^(2)`, the Y-axis and the straight line y = 5 is given by

A

`(14)/(3)` sq units

B

`(7)/(3)` sq units

C

5 sq units

D

`(16)/(3)` sq units

Text Solution

Verified by Experts

The correct Answer is:
D
`therefore` Put x = 0, in `y = 1+x^(2), y = 1`
Required area `=int_(1)^(5)xdy=int_(1)^(5)sqrt(y-1)dx`

`=[((y-1)^(3//2))/(3//2)]_(1)^(5)=(2)/(3)[(4)^(3//2)-0]`
`=(16)/(3)` sq units
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