Finding the definite integral

Question

I need some help figuring out how to answer this problem:

1. Let 𝑘 be a real number such that 0 < 𝑘 < 1. Find the following definite integral:
2. The boundaries are from 0 to pi
3. The ∫dt/(1+(k)cos(t))^2

Answer 1

First, distribute the integrand:

int 0^pi (1+2kcos(t)+k^2cos^2(t)) dt.

Now, integrate term-by-term. You can use the identity cos^2(t) = 0.5*(1+cos(2*t)).