Compute the area of the figure bounded by the straight lines `x=0,x=2` and the curves`y=2^x ,y=2x-x^2`

Explanation

We have to find the area of the region bounded by
the
straight lines `x=0,x=2`
and
the curves`y=2^x ,y=2x-x^2`
so area is,
`A=int_0^2(2^x-2x+x^2)dx`
`=[2^x/ln(2)+((x-3)x^2)/3]_0^2`
`=[4/ln2-4/3]-[1/ln2]`
`=3/log 2-4/3`