Solve Integral w/ Change of Variable Technique

[Stumped1]

How would I apply the change of variable technique to solve the integral
\(\displaystyle \int x\frac{2x}{1000^2}e^{-(x/1000)^2}dx\)

w/ out the \(\displaystyle x\) I used
\(\displaystyle u=(x/1000)^2\) , and \(\displaystyle du=2x/1000^2\)

Now, I am calculating \(\displaystyle E(x)\), and now sure how to deal w/ the extra \(\displaystyle x\).

Thanks for any help!

 

[Aryth1]

How would I apply the change of variable technique to solve the integral
\(\displaystyle \int x\frac{2x}{1000^2}e^{-(x/1000)^2}dx\)

w/ out the \(\displaystyle x\) I used
\(\displaystyle u=(x/1000)^2\) , and \(\displaystyle du=2x/1000^2\)

Now, I am calculating \(\displaystyle E(x)\), and now sure how to deal w/ the extra \(\displaystyle x\).

Thanks for any help!

The key is that substitution works both ways.

First, you let $u = \left(\frac{x}{1000}\right)^2$. So, what does that make $x$ equal to?