Solution Found!
Using symmetry Use symmetry to evaluate the following
Chapter 7, Problem 49E(choose chapter or problem)
Using symmetry Use symmetry to evaluate the following integrals.
a. \(\int_{-\infty}^{\infty} e^{-|x|} d x\) b. \(\int_{-\infty}^{\infty} \frac{x^{3}}{1+x^{8}} d x\)
Questions & Answers
QUESTION:
Using symmetry Use symmetry to evaluate the following integrals.
a. \(\int_{-\infty}^{\infty} e^{-|x|} d x\) b. \(\int_{-\infty}^{\infty} \frac{x^{3}}{1+x^{8}} d x\)
ANSWER:SOLUTION
We have to use symmetry to evaluate the given integrals.
A function is said to be even when
A function is said to be odd when
Therefore if a function is even,then
If a function is odd ,then
Step 1
(a).
Here we can see that .therefore this is a positive function.
Thus we can write