AP EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \frac{1}{1+\tan ^{2020}(x)} d x=\)
- A \(\pi\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{4}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\[ I=\int_0^{\pi / 2} \frac{d x}{1+\tan ^{2020} x}=\int_0^{\pi / 2} \frac{\cos ^{2020} x}{\cos ^{2020} x+\sin ^{2020} x} d x \] On applying property \(\int_0^a f(x) d x=\int_0^a f(a-x) d x\), we get…
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