Dirac Delta Function Integral
Im having some trouble with the following question:
"Evaluate the integral: e^x [dirac(x + 1) − dirac(x − 2)] dx from -ve infinity to 1"
Am i supposed to use a Laplace transformation? In which case I split it into 2 integrals:
e^x * dirac(x + 1)
e^x * dirac(x − 2) dx
So for the first integral I get exp(p-1), and for the second exp(2-2p). So overall exp(p-1) - exp(2-2p).
However as the original integral was from -ve infinity to 1, the second dirac integral (at x=2) would be out of this boundary. So would I disregard this?
Have I gone about this problem in the correct way?
Thanks in advance.