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Q.

The value of ∫0π/2 dx1+tan3⁡ x is

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a

0

b

1

c

π/4

d

π/2

answer is C.

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Detailed Solution

I=∫0π/2 dx1+tan3⁡ x=∫0π/2 dx1+tan3⁡ (π/2−x)=∫0π/2 dx1+cot3⁡ x=∫0π/2 tan3⁡ x1+tan3⁡ xdx=∫0π/2 1−11+tan3⁡ xdx=π2−I.Thus I=π/4.

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