TS EAMCET · Maths · Definite Integration
If \(I=\int_0^{\pi / 2} \frac{d x}{5+3 \sin x}=\lambda \tan ^{-1}\left(\frac{1}{2}\right)\), then \(\lambda=\)
- A \(\frac{1}{4}\)
- B 1
- C \(\frac{1}{2}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \[ I=\int_0^{\pi / 2} \frac{d x}{5+3 \sin x}=\lambda \tan ^{-1}\left(\frac{1}{2}\right) \] Now, \(I=\int_0^{\pi / 2} \frac{d x}{5+3 \sin x}\)…
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