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

The area of the region bounded by the curve `y = 2x - x^2` and the line `y = x` is

A

`(1)/(6)`

B

`(1)/(2)`

C

`(1)/(3)`

D

`(7)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
A
The intersection points of given curves are (0,0) and (1,1)
`therefore` Required area `=int_(0)^(1)[(2x-x^(2))-x]dx`
`=int_(0)^(1)(x-x^(2))dx=[(x^(2))/(2)-(x^(3))/(3)]_(0)^(1)`

`=(1)/(6)` sq. unit
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