TS EAMCET · Maths · Definite Integration
\(\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x\) is equal to :
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x\) Put \(x=\cos \theta \Rightarrow d x=-\sin \theta d \theta\) \(\therefore \quad I=\int_{\pi / 2}^0 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+\cos \theta}{1-\cos \theta}}\right)(-\sin \theta) d \theta\)…
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