- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Here's this week's problem.
-----
Problem: For $a>1$, show that\[\int_0^{2\pi}\frac{\,d\theta}{(a+\cos\theta)^2} = \frac{2\pi a}{(a^2-1)^{3/2}}.\]
-----
Hint:
Remember to read the POTW submission guidelines to find out how to submit your answers!
-----
Problem: For $a>1$, show that\[\int_0^{2\pi}\frac{\,d\theta}{(a+\cos\theta)^2} = \frac{2\pi a}{(a^2-1)^{3/2}}.\]
-----
Hint:
Use the substitution $z=\exp(i\theta)$ to rewrite the definite integral as a contour integral over the unit circle $|z|=1$.
Remember to read the POTW submission guidelines to find out how to submit your answers!