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Definite Integration
Properties of Definite Integrals
JEE Main 2021
Grade 12

Question:

$\int_0^\pi \frac{x}{1 + \sin x} \, dx$ equals:
(1) $\pi$
(2) $2\pi$
(3) $\frac{\pi}{2}$
(4) $\frac{\pi^2}{2}$

Step-by-Step Solution

Key Concept: Apply $\int_0^\pi f(x) \, dx = \int_0^\pi f(\pi - x) \, dx$, add this to the original integral, and you will be left with an integral of $\frac{1}{1 + \sin x}$ alone.
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Correct Answer: (1)

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