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The area between y=tanx and X- axis from x=0 to x=π4

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a
π4
b
22
c
log2
d
log2

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detailed solution

Correct option is D

The given curve is y=tanx

The rough sketch of the required area is as shown below

 

The required area is the area of the shaded region.

The area of the shaded region is the area of the region bounded by the curve y=tanxx=0 and x=π4 with X- axis

Hence the area of the shaded region is A=0π4tanxdx

A=0π4tanxdx =logsecx0π4 =log2-log1 =log2

Therefore, the area of shaded region is log2

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