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TS EAMCET · Maths · Definite Integration

\(\int_0^{\frac{\pi}{2}} \sqrt{\tan x} d x=\)

  1. A \(\frac{\pi}{\sqrt{2}}\)
  2. B \(\frac{\pi}{2}\)
  3. C \(\sqrt{2} \pi\)
  4. D \(2 \pi\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\pi}{\sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\int_0^{\frac{\pi}{2}} \sqrt{\tan x} d x = \frac{1}{2} B\left(\frac{1/2+1}{2}, \frac{-1/2+1}{2}\right) = \frac{1}{2} B\left(\frac{3}{4}, \frac{1}{4}\right) = \frac{1}{2} \frac{\Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{1}{4}\right)}{\Gamma\left(\frac{3}{4} +…