AP EAMCET · Maths · Indefinite Integration
If \(\mathrm{I}_{\mathrm{n}}=\int_0^{\frac{\pi}{4}} \tan ^n x d x\), then \(\mathrm{I}_{13}+\mathrm{I}_{11}=\)
- A \(\frac{1}{13}\)
- B \(\frac{1}{12}\)
- C \(\frac{1}{10}\)
- D \(\frac{1}{11}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{12}\)
Step-by-step Solution
Detailed explanation
Given, \(I_n=\int_0^{\pi / 4} \tan ^n x d x\) and \(I_{n+1}=\int_0^{\pi / 4} \tan ^{n+1} x d x \quad(n \rightarrow n+1)\) \(I_{n-1}=\int_0^{\pi / 4} \tan ^{n-1} x d x \quad(n \rightarrow n-1)\) Since, we know…
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