WBJEE · Maths · Definite Integration
The value of \(\int_0^{\infty} \frac{d x}{\left(x^2+4\right)\left(x^2+9\right)}\) is
- A \(\frac{\pi}{60}\)
- B \(\frac{\pi}{20}\)
- C \(\frac{\pi}{40}\)
- D \(\frac{\pi}{80}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{60}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hints : } \left.\int_0^{\infty} \frac{\mathrm{dx}}{\left(\mathrm{x}^2+4\right)\left(\mathrm{x}^2+9\right)}=\int_0^{\pi / 2} \frac{\sec ^2 \theta}{\left(\tan ^2 \theta+4\right)\left(\tan ^2 \theta+9\right)} \mathrm{d} \theta \text { (putting }…
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