Numerical Evaluation of the Integral: e^-it J0(2t)

[CalcYouLater]

Homework Statement

Evaluate:

$$\int_{0}^{\infty}e^{-it}J_{0}(2t)dt$$

to a numerical value

Homework Equations

The Attempt at a Solution

Well, I went to the tables for this one and came up empty handed. I found an integral in a table that is almost this integral. The problem is that the integral I found cannot have an exp(-it) term in it...it only allows for exp(+it) terms.

 

[fzero]

Well, I went to the tables for this one and came up empty handed. I found an integral in a table that is almost this integral. The problem is that the integral I found cannot have an exp(-it) term in it...it only allows for exp(+it) terms.

Try taking the complex conjugate of the integral formula.

 

[CalcYouLater]

Thanks for the reply. It turns out that the table I was using had a mistake in it. I used mathematica to compute the integral.