# Splitting an integral with an absolute value

This is a physics problem, but I only need help with the calculus portion of it. I was having trouble figuring out how to split the integral to properly integrate.

## Homework Equations

$$\int$$$$\stackrel{\infty}{-\infty}$$(x/x_0)e-2|x|/x_0dx

where x_o is a constant

## The Attempt at a Solution

I was wondering how to write the lower part of the integral. What I have is

$$\int$$$$\stackrel{0}{-\infty}$$(x/x_0)e2x/x_0dx+$$\int$$$$\stackrel{\infty}{0}$$(x/x_0)e-2x/x_0dx

Is that right or should I keep the negative in front of the 2 in the lower integral?

## The Attempt at a Solution

Dick
Homework Helper
You've got it right. But there is an easy way to do your integral. If f(x) is the integrand, how does f(x) compare with f(-x)?

Mark44
Mentor
Fixed the LaTeX in your first integral. Double-click it to see what I did.
Here are some tips:
Use only a single pair of [ tex] and [ /tex] tags (without the leading spaces that I show) for a given expression. You had tex tags around almost every item.
Don't mix [ sup] and [ sub] tags inside [ tex] tags. They don't work. Instead use ^{} for superscripts and _{} for subscripts.
This is a physics problem, but I only need help with the calculus portion of it. I was having trouble figuring out how to split the integral to properly integrate.

## Homework Equations

$$\int_{-\infty}^{\infty}(x/x_0)e^{-2|x|/x_0} dx$$

where x_o is a constant

## The Attempt at a Solution

I was wondering how to write the lower part of the integral. What I have is

$$\int$$$$\stackrel{0}{-\infty}$$(x/x_0)e2x/x_0dx+$$\int$$$$\stackrel{\infty}{0}$$(x/x_0)e-2x/x_0dx

Is that right or should I keep the negative in front of the 2 in the lower integral?

## The Attempt at a Solution

Fixed the LaTeX in your first integral. Double-click it to see what I did.

Thanks for the fix. I was struggling with it :P

You've got it right. But there is an easy way to do your integral. If f(x) is the integrand, how does f(x) compare with f(-x)?

I was thinking I could just double the integral from 0 to $$\infty$$ but because there was an x/x_0 in front and I would have to integrate by parts, I reasoned against it.

I wouldn't know how else to simplify it.

Dick
I was thinking I could just double the integral from 0 to $$\infty$$ but because there was an x/x_0 in front and I would have to integrate by parts, I reasoned against it.