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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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