TS EAMCET · Maths · Definite Integration
\(\int_0^\pi \frac{1}{1+\sin x} d x\) is equal to
- A 1
- B 2
- C -1
- D -2
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int_0^\pi \frac{1}{1+\sin x} d x \\ & =\int_0^\pi \frac{1}{1+\frac{2 \tan \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}} d x \\ & =\int_0^\pi \frac{\sec ^2 \frac{x}{2}}{\left(1+\tan \frac{x}{2}\right)^2} d x \\ & \text { Put } \tan \frac{x}{2}=t…
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