- #1
slugbunny
- 15
- 0
Homework Statement
Use
1) [itex]\frac{1}{2\pi}\int\limits_{-\pi}^{\pi} \frac{r_0^2 - r^2}{r_0^2 - 2rr_0cos(\theta-t) + r^2} dt = 1[/itex]
to compute the integral:
2) [itex]\int\limits_{-\pi}^{\pi} \left[1 - acos(x) \right]^{-1} dx[/itex]
for [itex]0<a<1[/itex]
[/itex].
The Attempt at a Solution
I looked on Wolfram for help. I did a tan substitution,
[itex]u = tan\left(\frac{x}{2}\right)[/itex]
and simplified
[itex]\int\limits_{-\pi}^{\pi} \left[1 - acos(x) \right]^{-1} dx \rightarrow \int\limits_{-\pi}^{\pi} \frac{2}{u^2+1-a+au^2}dx[/itex]
It kind of looks like 1)...? I am pretty confused.
Thanks in advance!