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Definite Integration
Properties of Definite Integrals
IIT-JEE 2013
Grade 12

Question:

$\int_0^{\pi/2} \frac{dx}{1 + \tan^3 x}$ equals:
(1) $\frac{\pi}{4}$
(2) $\frac{\pi}{2}$
(3) $\frac{\pi}{8}$
(4) $0$

Step-by-Step Solution

Key Concept: Use the King's-rule property $\int_0^a f(x) \, dx = \int_0^a f(a - x) \, dx$ with $a = \pi/2$, and add the two equal forms of the integral.
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Correct Answer: (1)

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