Fourier Transform in the Form of Dirac-Delta Function

[Captain1024]

Homework Statement

Given x(t)=8cos(70\pi t)+4sin(132\pi t)+8cos(24\pi t), find the Fourier transform X(f) in the form of \delta function.

Homework Equations

X(f)=\int ^{\infty}_{-\infty}x(t)e^{-j\omega _0t}dt
cos(\omega t)=\frac{e^{j\omega t}+e^{-j\omega t}}{2}
sin(\omega t)=\frac{e^{j\omega t}-e^{-j\omega t}}{2j}
\int ^{\infty}_{-\infty}cos(\omega _0t)e^{-j\omega t}dt=\frac{\pi}{2}(\delta (\omega +\omega _0)+\delta (\omega -\omega _0))
\int ^{\infty}_{-\infty}sin(\omega _0t)e^{-j\omega t}dt=\frac{\pi}{j2}(\delta (\omega +\omega _0)-\delta (\omega -\omega _0))

The Attempt at a Solution

X(f)=\frac{8\pi}{2}(\delta (\omega +70\pi)+\delta (\omega -70\pi))+\frac{4\pi}{j2}(\delta (\omega +132\pi)-\delta (\omega -132\pi))+\frac{8\pi}{2}(\delta (\omega +24\pi)+\delta (\omega -24\pi))

Simplifying: X(f)=4\pi (\delta (\omega +70\pi)+\delta (\omega -70\pi))+\frac{2\pi}{j} (\delta (\omega +132\pi)-\delta (\omega -132\pi))+4\pi (\delta (\omega +24\pi)+\delta (\omega -24\pi))

 

[rude man]

All clear, Captain!
(You could changew +1/2j to -j/2 but that would be quibbling!)
Nice work.