- #1
Vitani11
- 275
- 3
Homework Statement
F(t) = sqrt(π/2)e-t for t>0
F(t) = sqrt(π/2)et for t<0
In other words the question asks to solve this integral: 1/sqrt(2π) ∫F(t)eitxdt and show that it equals 1/(1+x2)
Homework Equations
F(t) = sqrt(π/2)e-t for t>0
F(t) = sqrt(π/2)et for t<0
1/sqrt(2π) ∫F(t)eitxdt
The Attempt at a Solution
I want to use complex numbers but these functions are analytic and so I can not do this using residues. A naive approach to integrating with respect to t is straightforward but the limits cause the result to be infinity. How should I approach this properly?