TS EAMCET · Maths · Definite Integration
\(\int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec (2023 x)}{1+(2023)^{(2023 x)}} d x=\)
- A \(\frac{1}{2023 \sqrt{2}}+c\)
- B \(\frac{\log (\sqrt{2}+1)}{2023}+c\)
- C \(\frac{\log 2}{4046}+c\)
- D \(\frac{\sqrt{2}}{2023}+c\)
Answer & Solution
Correct Answer
(B) \(\frac{\log (\sqrt{2}+1)}{2023}+c\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec 2023 x}{1+(2023)^{(2023 x)}} d x\) Using \(f(x) \rightarrow f(a+b-x)\) ...(1) \[ \Rightarrow I=\int_{\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec 2023 x}{1+(2023)^{-2023 x}} d x \]…
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