TS EAMCET · Maths · Definite Integration
\(\int_{-\pi / 15}^{\pi / 15} \frac{\cos 5 x}{1+e^{5 x}} d x=\)
- A \(\frac{1}{5}\)
- B \(\frac{\sqrt{3}}{10}\)
- C \(\frac{1}{15}\)
- D \(\frac{1}{10}\)
Answer & Solution
Correct Answer
(B) \(\frac{\sqrt{3}}{10}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & I=\int_{-\frac{\pi}{15}}^{\frac{\pi}{15}} \frac{\cos 5 x}{1+e^{5 x}} d x \Rightarrow I=\int_0^{\frac{\pi}{15}} \frac{\cos 5 x}{1+e^{5 x}} d x+\int_0^{\frac{\pi}{15}} \frac{\cos (-5 x)}{1+e^{(5(-x))}} d x \\ = & \int_0^{\frac{\pi}{15}} \frac{\cos 5 x}{1+e^{5 x}}…
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