AP EAMCET · Maths · Definite Integration
\(\int_{\pi / 6}^{\pi / 3} \frac{1}{1+\sqrt{\cot x}} d x=\)
- A \(\frac{\pi}{12}\)
- B \(\frac{\pi}{6}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{13}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{12}\)
Step-by-step Solution
Detailed explanation
\(\int_{\pi / 6}^{\pi / 3} \frac{1}{1+\sqrt{\cot x}} d x=I\) \[ I=\int_{\pi / 6}^{\pi / 3} \frac{\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x \] We have, \(\int_a^b f(x) d x=\int_a^b f(a+b-x) d x\)…
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