Fourier series and calculate integral

[rayman123]

Homework Statement

expand the function in Fourier series and calculate the integral
$$f(x)= (sinx)^2(cosx)^3, 2\pi$$ is the period
calculate the integral
$$\int_{0}^{2\pi}f(x)dx$$
please help...have absolutely no idea how to calculate it...

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Express the cos³(x) as (1 - sin²(x))cos(x) and use the substitution u = sin(x).

 

[vela]

Homework Statement

expand the function in Fourier series and calculate the integral
$$f(x)= (sinx)^2(cosx)^3, 2\pi$$ is the period
calculate the integral
$$\int_{0}^{2\pi}f(x)dx$$
please help...have absolutely no idea how to calculate it...

Note that f(x) is even, so what does this tell you about its Fourier expansion?

You can use trig identities to rewrite f(x) as a Fourier series, instead of having to crank out the integrals. In particular, look at the power-reduction formulas, and use what you know about what its Fourier expansion should look like to guide you.

http://en.wikipedia.org/wiki/List_of_trigonometric_identities