# Homework Help: Tricky Integral (fourier transforms)

1. Nov 19, 2008

### wolf party

the question is on fourier transforms and i am stuck on how to approch the integral

INT[ (1/(2*pi))*e^(ik(x-y)-(1+ik)ct) dk

i know that the integral INT [(1/(2*pi))*e^(ik(x-y-ct)) dk] yields the delta function

= DELTA(x-y-ct) but the terms in the exponential from the integral in question have stumped me

any ideas would be great, cheers

2. Nov 19, 2008

### Pere Callahan

What don't you like about the delta function result?

The e-ct is just a constant...

3. Nov 19, 2008

### wolf party

would that mean we now have

(INT[e^-ct]) *DELTA(x-y-ct) ?

4. Nov 19, 2008

### Pere Callahan

No, the integral is gone, but the constant still there. What you end up with is

e-ctDelta(x-y-ct)

5. Nov 19, 2008

### wolf party

cheers

from that, the integral goes into the second integral

u(x,t)=[INT (u(y, 0)dy*e^-ct*DELTA(x-y-ct))] - integrated over real space

does this equal e^-ct*u(x-ct,0) ?

6. Nov 19, 2008

Yes.