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Question

The value of π015+4 cos xdx is

A
π
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B
π2
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C
π3
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D
π4
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Solution

The correct option is C π3
We have,Let I=π015+4 cos xdx=π015+4 1tan2 x21+tan2 x2dx=π01+tan2 x25(1+tan2 x2)+4 (1tan2 x2)dx=π0sec2 x29+tan2 x2dxLet tan (x2)=t12sec2 x2dx=dtAlso, x=0t=0 and x=πt=I=0sec2 x29+t2×2sec2 x2dtI=2019+t2dt=20132+t2dtI=2 (tan1(t3)3]0=23(tan1(t3)]0I=23(tan1()tan1(0)]I=23(π20)I=π3

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