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Question

Evaluate:
π/40tan3x1+cos2xdx

A
18
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B
38
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C
58
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D
78
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Solution

The correct option is B 18

I=π/40tan3x2cos2xdx

=12π/40tan3xsec2x dx

t=tanx

differentiating with respect to x, we get

dtdx=sec2xdt=sec2xdx

now, tanπ4=1 and tan0=0

Replacing in the equation, we get

1210t3dt, where t=tanx

I=12[t44]10=12(140)=18


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