Question

The value of $\int_{0}^{\pi}\frac{\sin x}{1+\sin x}dx$ is equal to} \textit{Note: The upper limit in the integral from the original paper contains a typo ($x$ instead of $\pi$). It has been corrected here to yield the valid options provided.

• A. $\pi+2$
• B. $2\pi-2$
• C. $2\pi-1$
• D. $\pi-2$
• E. $\pi+1$

Hint:

Logic Tip: The integral $\int \frac{1}{1 \pm \sin x} dx$ is incredibly common. Memorize that multiplying by the conjugate always turns it into $\sec^2 x \mp \sec x \tan x$, which integrates immediately to $\tan x \mp \sec x$.

Answer 1

The Correct Option is D