Help with integral


by jaygatsby
Tags: integral
jaygatsby
jaygatsby is offline
#1
Jan27-13, 10:29 AM
P: 3
This is not a homework problem, but a problem in the textbook that is not required. I am doing this to get a handle on the topic.

I am evaluating a Fourier transform, without tables, and need to evaluate this integral:

[tex]
\int e^{-t} * sin(2 \pi f_c t) * e^{-j2 \pi ft} dt
[/tex]

I have tried two methods: 1) integration by parts, and 2) integration after expressing the sine function as a complex exponentials. I get stuck in both cases.

The asterisks are there to assist with clarity of spacing. Thanks for any help you can provide,
J
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mathman
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#2
Jan27-13, 04:06 PM
Sci Advisor
P: 5,941
Use Euler formula to get exp(-t)*trig function. This is a standard integral (find in table).

Trig function: sin(at), integral = a/(1 + a2)
cos(at), integral = 1/(1 + a2)
(a > 0 for both)
jaygatsby
jaygatsby is offline
#3
Jan27-13, 06:49 PM
P: 3
Thanks, I did try Euler's formula but then worked the integral out manually (attempted to...)

So this integral I would find in the table exclusively, and never try without a table? The way the drill is stated in the book (not a homework problem.), I wonder if I am to work it out without a table.

Thanks,
J

mathman
mathman is offline
#4
Jan28-13, 02:32 PM
Sci Advisor
P: 5,941

Help with integral


You can integrate by parts twice to get an equation involving the original integral.

I(exp(-t)cos(at)) = 1 + aI(exp(-t)sin(at)) = 1 - a2I(exp(-t)cos(at))

Similarly for sin(at) integral.
jaygatsby
jaygatsby is offline
#5
Jan28-13, 04:22 PM
P: 3
Thank you


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