How would you solve this? math
Hello!
How would you calculate this inner product? (a.k.a. calculate the integral)
Image: http://dl.dropbox.com/u/41504745/CodeCogsEqn%20%287%29.gif
Plaintext: int((xsinx)/e^(x^2)dx) from -infinity to +infinity
Thanks!
November 23, 2011
5 Comments • Newest first
Okay, I solved this during my physics lecture. I'll post the work once I get back to my dorm, if no one else has. Just gonna sit through my math lecture now.
Edit: [url=http://i286.photobucket.com/albums/ll92/cb000/GaussianIntegration1.png]Here it is.[/url]
I just noticed that the very last integral that added to zero is off by a factor of 1/2, but it doesn't matter because it's zero nevertheless.
ouch
Gotta head to class now, but one method I can see is converting the sin(x) to (e^ix-e^-ix)/(2i) and then completing the square to get two Gaussian integrals.
It's a trick I use often for doing Fourier Transforms in physics.
@RealSheep:
Yes, I need to use integration by parts but I just don't know how. Using wolfram alpha is pretty much useless because it's not homework or anything like that, I need to understand how to solve the problem because I'm studying for my test on friday.
Here is the answer; http://www.wolframalpha.com/input/?i=int%28%28xsinx%29%2Fe%5E%28x%5E2%29dx%29+-inf+to+inf but that's not what I'm asking for. I wanna know how to do all the steps in the integration.
I wouldn't, i would just go with the classic "my dog ate my homework"