JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{k \pi}{16}\), then \(k\) is equal to \(...........\).
- A \(29\)
- B \(26\)
- C \(25\)
- D \(28\)
Answer & Solution
Correct Answer
(B) \(26\)
Step-by-step Solution
Detailed explanation
\(I=\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right)}{1+5^{\cos x}} d x\) \(I=\int \limits_0^\pi \frac{5^{-\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right)}{1+5^{-\cos x}} d x\)…
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