# Fourier series and calculate integral

1. May 27, 2010

### rayman123

1. The problem statement, all variables and given/known data
expand the function in Fourier series and calculate the integral
$$f(x)= (sinx)^2(cosx)^3, 2\pi$$ is the period
calculate the integral
$$\int_{0}^{2\pi}f(x)dx$$

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 27, 2010

### LCKurtz

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

3. May 27, 2010

### vela

Staff Emeritus
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