TS EAMCET · Maths · Definite Integration
\(\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cot ^9 x d x=\)
- A \(\frac{-7}{42}+\frac{1}{2} \log 2\)
- B \(\frac{7}{24}-\frac{1}{2} \log 2\)
- C \(\frac{25}{24}+\frac{1}{2} \log 2\)
- D \(\frac{1}{24}+2 \log 2\)
Answer & Solution
Correct Answer
(A) \(\frac{-7}{42}+\frac{1}{2} \log 2\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & I=\int_{\pi / 4}^{\pi / 2} \cot ^9 x d x \\ & I=\int_{\pi / 4}^{\pi / 2} \frac{\cos ^9 x}{\sin ^9 x} d x \end{aligned} \] Put \(\sin x=t, \cos x d x=d t\)…
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