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The area enclosed between the curves y=x...

The area enclosed between the curves `y=x and y=2x-x^(2)` (in square units), is

A

`(1)/(2)`

B

`(1)/(6)`

C

`(1)/(3)`

D

`(1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)/(2)-(1)/(3)=(1)/(6)` sq unit
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