I have become stuck while trying to evaluate the following trigonometric integral:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_0^{\pi} (A + B \sin x)^n dx.[/itex]

First, I have tried to find a recurrence with respect ton, from which the closed-form solution could be calculated. However, I have failed to do this. Similarly, my effort to solve the integral using the binomial theorem seems to be useless, since this leads to the sum that I find relatively hard to evaluate.

So my next thoughts have been to find an asymptotic approximation of this integral, forntending to infinity. However, I have found that I am unable to do this with my very basic background in asymptotic analysis.

Thus, my question is: could anybody suggest me how to achieve the above mentioned asymptotic approximation (I don't believe in a reasonable closed-form solution of this integral, so I am not asking for any)?

Thank you in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Asymptotics for a trigonometric integral

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**