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Area of the region bounded by the curves...

Area of the region bounded by the curves `y=2^(x),y=2x-x^(2),x=0" and "x=2` is given by :

A

`3//log2-4//3" sq unit"`

B

`3//log2+4//3" sq unit"`

C

`3log2+4//3" sq unit"`

D

`3log2-4//3" sq unit"`

Text Solution

Verified by Experts

The correct Answer is:
A
The two curves `y=2^(x)" "…(i)`
and `" "y=2x-x^(2)" "…(ii)`
do not intersect between x = 0 and x = 2

`:.` Required area `=int_(0)^(2)(2^(x)-2x-x^(2))dx`
`=3//log2-4//3" sq units"`
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