Math Help - Solve the integral problem.......

1. Solve the integral problem.......

Can anyone solve the problem given in the attachment? here a, b and 2pi are constants. Please show the steps while u solve it.

Bye.

2. What did you get so far and is this what it looks like?

$\frac{1}{a2\pi}\int_{-\infty}^{\infty} ye^{(\frac{-y^2}{b})}~dy$

$\frac{-be^{(\frac{-y^2}{b})}}{a4\pi}\bigg|^{\infty}_{-\infty}$

3. the function is odd (f(-x)=-f(x)), so the integral is zero.

4. Well I want to test the previous post. If it's true then i'm going to have a lot less work to do!

$\frac {1}{a(2 \pi)}\int_{-\infty}^{+\infty}ye^{ \frac {-y^2}{b}}dy$

$u=\frac {-y^2}{b}$

$\frac {du}{dy}=\frac{-2y}{b}$

$dy= \frac {b du}{-2y}$

The limits remain the same. I do not think it is necessary to write that part of the working out.

$\frac{1}{a(2 \pi)(-2)}\int_{- \infty}^{\infty} \frac {y}{y}udu$

$\frac{1}{-4a \pi}\int_{- \infty}^{\infty} udu$

$\frac {1}{-4a \pi} [\frac{u^2}{2}]^{\infty}_{-\infty}$

$\frac {1}{-8a \pi}[u^2]^{\infty}_{-\infty}$

$\frac {1}{-8a \pi}((\infty)^{2}-(-\infty)^{2})$

$\frac {1}{-8a \pi}(0)=0$

WOW! That is the find of the century for me!!!!

(oh, and that's how I would integrate it.)

5. showcase, you have two mistakes in your arguments -- namely, with "the limits stay the same", and after the change of variables you lost exponential for some reason.

basically 11rdc11 wrote out the solution -- the primitive is $\frac{-be^{(\frac{-y^2}{b})}}{a4\pi}$ and then the integral is $\lim_{y\to\infty}\frac{-be^{(\frac{-y^2}{b})}}{a4\pi}-\lim_{y\to -\infty}\frac{-be^{(\frac{-y^2}{b})}}{a4\pi}=0$.

the short way of this, as I said, is to note that the function is odd, so the integral is zero immediately, though I am sloppy here, because for this argument to work, one needs to check that the integral is finite at first

6. Originally Posted by choovuck
the function is odd (f(-x)=-f(x)), so the integral is zero.

Lol I forgot about it being odd. It would have saved me some work

7. Good point!

I was doing that late last night and still getting the hang of Latex. :s