Question:
The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is
The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is
Updated On: Jun 18, 2022
- $e^{a^2}$
- $0$
- $e^{-a^2}$
- $a$
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The Correct Option is B
Solution and Explanation
Since, $\frac{xe^{x^2}}{1+x^{2}}$ is an odd function.
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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.
