Question

\( \int_{\pi/4}^{3\pi/4} \frac{x}{1+\sin x} \, dx \) is equal to

• A. \( \pi(\sqrt{2}-1) \)
• B. \( \pi(\sqrt{2}+1) \)
• C. \( 2\pi(\sqrt{2}-1) \)
• D. \( 2\pi(\sqrt{2}+1) \)
• E. \( \frac{\pi}{\sqrt{2}+1} \)

Hint:

For integrals involving \(x\) in numerator, always try \(x \to a+b-x\) substitution to exploit symmetry.

Answer 1

The Correct Option is B