Sketch the curves and identify the region bounded by the curves `x=1/2,x=2,y=logxa ny=2^xdot` Find the area of this region.

Explanation

`A` is point of intersection of `x = 1/2` and` y = 2x`.
So, `A` is `(1/2, 2)`.
`B` is point of intersection of `x = 1/2` and `y = lnx`.
So,` B` is `(1/2, - ln2)`.
`C` is point of intersection of `x = 2` and `y = In x`.
So,` C` is `(2, In2)`.
` D` is point of intersection of `x = 2` and `y = 2x`.
So,` D` is `(2, 4)`.
Area `ABCD=int_(1/2)^2(y_1-y_2)dx`
`=int_(1/2)^2(2^x-ln x)dx`
`=[2^x/ln 2]_(1/2)^2-[x lnx-x]_(1/2)^2`
`=4/ln 2-sqrt2/ln 2-(2 ln 2-2)+1/2ln 1/2-1/2`
`=(4-sqrt2)/ln 2+3/2-(5/2)ln 2`sq.units.