TS EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 4}[\sqrt{\tan x}+\sqrt{\cot x}] d x\) is equal to
- A \(\frac{\pi}{\sqrt{2}}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{3 \pi}{\sqrt{2}}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & I=\int_0^{\pi / 4} \sqrt{\tan x}+\sqrt{\cot x} d x \\ &=\int_0^{\pi / 4}\left(\frac{\sqrt{\sin x}}{\sqrt{\cos x}}+\frac{\sqrt{\cos x}}{\sqrt{\sin x}}\right) d x \\ &=\int_0^{\pi / 4} \frac{\sin x+\cos x}{\sqrt{\sin x \cos x}} d x \\ &=\int_0^{\pi / 4}…
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