MHT CET · Maths · Definite Integration
\(\int_{\frac{1}{2}}^2 \frac{1}{x} \operatorname{cosec}^{101}\left(x-\frac{1}{x}\right) \mathrm{d} x=\)
- A 0
- B 1
- C \(\frac{1}{4}\)
- D \(\frac{101}{2}\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Let \( I = \int_{\frac{1}{2}}^2 \frac{1}{x} \operatorname{cosec}^{101}\left(x-\frac{1}{x}\right) \mathrm{d} x \) Substitute \( x = \frac{1}{t} \implies \mathrm{d} x = -\frac{1}{t^2} \mathrm{d} t \)
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