Question:
Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx
= $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then
$ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is
Given that $ \int_{0}^{\infty}\frac{x^{2}}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)\left(x^{2}+c^{2}\right)} $ dx
= $ \frac{\pi}{2\left(a+b\right)\left(b+c\right)\left(c+a\right)'} $ then
$ \int_{0}^{\infty}\frac{dx}{\left(x^{2}+4\right)\left(x^{2}+9\right)} $ is
Updated On: Jun 14, 2022
- $ \frac{\pi}{60} $
- $ \frac{\pi}{20} $
- $ \frac{\pi}{40} $
- $ \frac{\pi}{80} $
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The Correct Option is A
Solution and Explanation
Answer (a) $ \frac{\pi}{60} $
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Concepts Used:
Integrals of Some Particular Functions
There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
Integrals of Some Particular Functions:
- ∫1/(x2 – a2) dx = (1/2a) log|(x – a)/(x + a)| + C
- ∫1/(a2 – x2) dx = (1/2a) log|(a + x)/(a – x)| + C
- ∫1/(x2 + a2) dx = (1/a) tan-1(x/a) + C
- ∫1/√(x2 – a2) dx = log|x + √(x2 – a2)| + C
- ∫1/√(a2 – x2) dx = sin-1(x/a) + C
- ∫1/√(x2 + a2) dx = log|x + √(x2 + a2)| + C
These are tabulated below along with the meaning of each part.
