TS EAMCET · Maths · Definite Integration
\(\int_{\pi / 5}^{3 \pi / 10} \frac{d x}{\sec ^2 x+\left(\tan ^{2022} x-1\right)\left(\sec ^2 x-1\right)}=\)
- A \(\frac{\pi}{20}\)
- B \(\frac{2 \pi}{5}\)
- C \(\frac{3 \pi}{20}\)
- D \(\frac{3 \pi}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{20}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}} \frac{d x}{1+\tan ^2 x+\left(\tan ^{2022} x-1\right) \tan ^2 x}\) \(\Rightarrow I=\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}} \frac{d x}{1+\tan ^{2024} x}\) ...(i)…
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