JEE Mains · Maths · STD 12 - 7.2 definite integral
For \(0 < a < 1\), the value of the integral \(\int_0^\pi \frac{\mathrm{d} x}{1-2 \mathrm{a} \cos x+\mathrm{a}^2}\)
- A \(\frac{\pi^2}{\pi+a^2}\)
- B \(\frac{\pi^2}{\pi-a^2}\)
- C \(\frac{\pi}{1-a^2}\)
- D \(\frac{\pi}{1+a^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{1-a^2}\)
Step-by-step Solution
Detailed explanation
\( I=\int_0^\pi \frac{d x}{1-2 a \cos x+a^2} ; 0 < a < 1 \) \( I=\int_0^\pi \frac{d x}{1+2 a \cos x+a^2} \) \( 2 I=2 \int_0^{\pi / 2} \frac{2\left(1+a^2\right)}{\left(1+a^2\right)^2-4 a^2 \cos ^2 x} d x \)…
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