Bladibla
- 357
- 1
Hi everyone,
I am new to Physics Forums so please excuse me - I am so embarrassed that I can't do this integral, but its quite urgent and so if anyone here could help me I would be much obliged!
The integral I must carry out is:
\int_{-\infty}^{\infty}e^{-ax^{2}}\,\text{cos}kx\,dx
I already know that the solution is
\sqrt{\frac{\pi}{a}}e^{-k^{2}/4a}
But the task is to find out how one can get to this answer...I think the hint is in:
\int_{-\infty}^{\infty}e^{-ax^{2}}\,dx =\sqrt{\frac{\pi}{a}}
which is from the standard Gaussian distribution.
Any information would be much appreciated!
Thank you,
Bladibla.
I am new to Physics Forums so please excuse me - I am so embarrassed that I can't do this integral, but its quite urgent and so if anyone here could help me I would be much obliged!
The integral I must carry out is:
\int_{-\infty}^{\infty}e^{-ax^{2}}\,\text{cos}kx\,dx
I already know that the solution is
\sqrt{\frac{\pi}{a}}e^{-k^{2}/4a}
But the task is to find out how one can get to this answer...I think the hint is in:
\int_{-\infty}^{\infty}e^{-ax^{2}}\,dx =\sqrt{\frac{\pi}{a}}
which is from the standard Gaussian distribution.
Any information would be much appreciated!
Thank you,
Bladibla.