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Sketch the curves and identify the regio...

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.

Text Solution

Verified by Experts

The correct Answer is:
`((4-sqrt(2))/(log2)-(5)/(2)log2+(3)/(2))` sq units
The required area is the shaded portion in following figure

`therefore ` The required area
` = int_(1//2)^(2) (2^(x)-log)dx = ((2^(x))/(log2)-(x logx -x))_(1//2)^(2)`
` = ((4-sqrt(2))/(log2)-(5)/(2)log2+(3)/(2))` sq units
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