TS EAMCET · Maths · Definite Integration
\(e^{\int_0^{\pi / 2} \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x}=\)
- A 1
- B \(2 \log 2\)
- C \(2 \log \sqrt{2}\)
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=e^{\int_0^{\pi / 2} \sqrt{\frac{1-\sin 2 x}{1+\sin 2 x}} d x}=e^{\int_0^{\pi / 2} \sqrt{\frac{(\cos x-\sin x)^2}{(\cos x+\sin x)^2}} d x} \\ & =e^{\int_0^{\pi / 2} \sqrt{\tan ^2\left(\frac{\pi}{4}-x\right) d x}}=e^{\int_0^{\pi / 2} \mid \tan…
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