# Homework Help: Deriving the fourier transform

1. Mar 11, 2015

### iScience

1. The problem statement, all variables and given/known data

derive the fourier sine and cosine transforms of $$f(x) = e^{-cx}$$ by using $$e^{iax}=cos(ax)+isin(ax)$$ and computing the integral $$\int_0 ^{\infty} e^{-cx}e^{iax}dx$$.

2. Relevant equations

3. The attempt at a solution

i'm completely clueless, all i did was evaluate what they told me to.

$$\int_0 ^{\infty} e^{-cx}e^{iax}dx = \int_0 ^{\infty} e^{(ia-c)x}dx$$
$$= \frac{e^{(ia-c)x}}{ia-c}\Big|_0^{\infty} = \frac{cos(ax)+isin(ax)}{ia-c}\Big|_0^{\infty} =-\frac{1}{ia-c}$$

Last edited: Mar 11, 2015
2. Mar 11, 2015

### Staff: Mentor

If you split your last result in imaginary and real part, you can relate it to the integrals in your other thread.