- #1
zeebek
- 27
- 0
This is not really a homework.
I am trying to solve one definite integral
[tex] \int_0^{2 \pi} \frac{\sin^2{t}}{\sqrt{a\cos{t} + b}} dt[/tex]
where [tex]a, b[/tex] are some positive numbers.
I tried integrate by parts, also differentiate by parameter [tex]a[/tex]. Does not help because of the square root. In this case I got some diff.equation for the integral I want, but I need to solve even more nasty integrals:
either
[tex] \int_0^{2 \pi} \sqrt{a\cos{t} + b} \cos{t} dt[/tex]
or
[tex] \int_0^{2 \pi} \frac{1}{\sqrt{a\cos{t} + b}} dt[/tex]
Homework Statement
I am trying to solve one definite integral
Homework Equations
[tex] \int_0^{2 \pi} \frac{\sin^2{t}}{\sqrt{a\cos{t} + b}} dt[/tex]
where [tex]a, b[/tex] are some positive numbers.
The Attempt at a Solution
I tried integrate by parts, also differentiate by parameter [tex]a[/tex]. Does not help because of the square root. In this case I got some diff.equation for the integral I want, but I need to solve even more nasty integrals:
either
[tex] \int_0^{2 \pi} \sqrt{a\cos{t} + b} \cos{t} dt[/tex]
or
[tex] \int_0^{2 \pi} \frac{1}{\sqrt{a\cos{t} + b}} dt[/tex]