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

The area of the figure bounded by the curves `y^(2)=2x+1` and `x-y-1=0` , is

A

`(2)/(3)` sq units

B

`(4)/(3)` sq units

C

`(8)/(3)` sq units

D

`(16)/(3)` sq units

Text Solution

Verified by Experts

The correct Answer is:
D
Given, curves are `y^(2)=2x+1` and x-y=1

Points of intersection are A(0, -1) and B(4, 3).
`therefore` Required area `=int_(-1)^(3)(1+y)dy-int_(-1)^(3)((y^(2)-1)/(2))dy`
`=[y+(y^(2))/(2)]_(-1)^(3)-[(1)/(2)((y^(3))/(3)-y)]_(-1)^(3)`
`=[3+(9)/(2)-(-1+(1)/(2))]-(1)/(2)[9-3-(-(1)/(3)+1)]`
`=8-(8)/(3)=(16)/(3)` sq units
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DEFINITE INTEGRALS -Exercise 2
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