TS EAMCET · Maths · Indefinite Integration
Let \(I_n=\int \sec ^n x d x\). If \(5 I_6-4 I_4=f(x)\), then \(f\left(\frac{\pi}{4}\right)\) is equal to
- A 2
- B 4
- C 1
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
Given that, \(I_n=\int \sec ^n x d x\) \(f(x)=5 I_6-4 I_4=5 \int \sec ^6 x d x-4 \int \sec ^4 x d x\) \(=\int 5 \sec ^4 x \sec ^2 x d x-\int 4 \sec ^2 x \sec ^2 x d x\) \(f(x)=\int\left\{5\left(1+\tan ^2 x\right)^2-4\left(1+\tan ^2 x\right)\right\} \sec ^2 x d x\) Let…
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