MHT CET · Maths · Indefinite Integration
The value of the integral \(\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{~d} x\) is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{8}\)
- D \(2 \pi\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Since } \int_0^{\frac{\pi}{2}} \frac{\cot ^{\mathrm{n}} x}{\tan ^{\mathrm{n}} x+\cot ^{\mathrm{n}} x} \mathrm{~d} x=\frac{\pi}{4} \\ & \int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{~d} x=\frac{\pi}{4}\end{aligned}\)
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