# Thread: In my notes i have this equals this

1. ## In my notes i have this equals this

But i have no idea how it does im getting a different answer, any help please?

2. Originally Posted by adam_leeds
But i have no idea how it does im getting a different answer, any help please?

$\displaystyle \frac{2}{2\pi}\int^a_0xe^{-x^2}\,dx=-\frac{1}{2\pi}\int^a_0(-2x\,dx)e^{-x^2}=$ $\displaystyle -\frac{1}{2\pi}\left[e^{-x^2}\right]^a_0=-\frac{1}{2\pi}\left[e^{-a^2}-e^0\right]$ $\displaystyle =\frac{1-e^{-a^2}}{2\pi}$ , so there's a mistake in your notes.

Tonio

3. Originally Posted by tonio
$\displaystyle \frac{2}{2\pi}\int^a_0xe^{-x^2}\,dx=-\frac{1}{2\pi}\int^a_0(-2x\,dx)e^{-x^2}=$ $\displaystyle -\frac{1}{2\pi}\left[e^{-x^2}\right]^a_0=-\frac{1}{2\pi}\left[e^{-a^2}-e^0\right]$ $\displaystyle =\frac{1-e^{-a^2}}{2\pi}$ , so there's a mistake in your notes.

Tonio
$\displaystyle \frac{2}{2 \pi } \int_0^a xe^{-x^2} dx$

Let $\displaystyle u=x^2$ and $\displaystyle du = 2xdx$

$\displaystyle \frac{1}{2 \pi } \int_0^{a^2} e^{-u} du = \frac{1}{2 \pi } [ e^{-a^2} - 1 ]$

I think you dont carry through your negative on the third step?

But the above is NOT equal to

$\displaystyle \frac{2}{ \sqrt{ \pi }} [ e^{-a^2} - 1 ]$

Your professor has messed up the constants somewhere along the way.

4. Originally Posted by AllanCuz
$\displaystyle \frac{2}{2 \pi } \int_0^a xe^{-x^2} dx$

Let $\displaystyle u=x^2$ and $\displaystyle du = 2xdx$

$\displaystyle \frac{1}{2 \pi } \int_0^{a^2} e^{-u} du = \frac{1}{2 \pi } [ e^{-a^2} - 1 ]$

I think you dont carry through your negative on the third step?

$\displaystyle \int e^{-u}\,du=-e^{-u}$ , and not only $\displaystyle e^{-u}$ . You forgot the minus sign here.

Tonio

But the above is NOT equal to

$\displaystyle \frac{2}{ \sqrt{ \pi }} [ e^{-a^2} - 1 ]$

Your professor has messed up the constants somewhere along the way.
.

5. So what I got from this thread was trust the judgment of MFH helpers over my own, always! lol thanks