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Find by integration the area of the regi...

Find by integration the area of the region bounded by the curve `y=2x-x^2` and the x-axis.

A

`(8)/(3)` sq units

B

`(4)/(3)` sq units

C

`(7)/(3)` sq units

D

`(2)/(3)` sq unit

Text Solution

Verified by Experts

The correct Answer is:
B
Given curve,
`y=2x-x^(2)`

For the intersection point of the curve and x-axis put y = 0
`therefore 2x-x^(2)=0`
implies x = 0,2
`therefore` The curve cut the X-axis at (0, 0) and (2, 0).
`therefore` Required area `=int_(0)^(2)(2x-x^(2))dx`
`=[x^(2)-(x^(3))/(3)]_(0)^(2)=[(2)^(2)-(2)^(2)/(3)-0]=4-(8)/(3)=(4)/(3)` sq units.
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