# Fourier Series Odd function

## Homework Statement

Determine a general Fourier series representation for f(x) = x^3 -1<x<1

## The Attempt at a Solution

May seem like a stupid Q, but would i have to calculate a0, an, bn or since i know that x^3 is an odd function, could jump straight into calculating the Fourier sine series for odd functions. Would that give me a general representation?

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if you calculate all the terms initially assuming the complete Fourier representation you will find that coefficients associated with the even terms will go to zero.
so its more like using a known result.

CompuChip
$$\int_{-1}^1 \cos(x) x^3 dx = \int_{-1}^0 \cos(x) x^3 dx + \int_0^1 \cos(x) x^3 dx = \int_0^1 \cos(-x) (-x)^3 dx + \int_0^1 \cos(x) x^3 dx = 0$$