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Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity

  • #1
1. Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity

I'm trying to understand how to use Fourier Transforms to solve Definite Integrals with limits from 0 to Infinity.
I understand how to use Fourier Transforms to solve indefinite integrals, but I believe there is supposed to be a much simpler way to solve these definite integrals without working out the entire indefinite solution.


Homework Equations


X(j0) = Integral from -Infinity to Infinity : x(t)dt
x(0) = Integral from -Infinity to Infinity: X(jw)dw
 

Answers and Replies

  • #2
marcusl
Science Advisor
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Welcome to PF! Here's a hint: Think about even and odd time functions.
 
  • #3
[tex]\displaystyle\int^\infty_0 2te^-^a^t\cos(t)\,dt = ?}[/tex]

I'm not entirely sure how to manipulate this.. the [tex]e^-^a^t[/tex] makes it so the function is neither even nor odd anymore.. even if I pulled the even part out to rewrite the function so its integrated from -infinity to infinity I'm unsure about what to do with the odd piece.
 
  • #4
marcusl
Science Advisor
Gold Member
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Yikes! I don't know what to do with this either. Sorry I jumped in...
 
  • #5
Yikes! I don't know what to do with this either. Sorry I jumped in...
I appreciate the thought! Thanks! :)
 

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