Dirac Delta Integrals: How to Solve for the Argument of the Delta Function?

[leroyjenkens]

Homework Statement

This is just an example, not a specific problem.

So if I have ∫σ(sinx), for example, and my limits of integration are, for example, 1 to 10, what I need to do to solve that is to find a value of x that would make the argument of the delta function 0. So for sinx, 0 makes the argument 0. But since it's outside of the limits of integration, the integral would be 0, correct? What if my limits of integration are 1 to 10, and I input pi as the argument for sine? I'm unsure of what to input in for the x, because I have 1 to 10 in the limits of integration, so does that mean I use degrees instead of radians?

Or for that one do I use the formula which is σf(x) = Ʃ σ(x-x_i)/|f'(x_i)|?
If f(x_i) = 0 and f'(x_i) does not = 0.

Using that formula, I still have to decide whether to use radians as my x (pi) or degrees (180).

Thanks.

 

[UltrafastPED]

But since it's outside of the limits of integration, the integral would be 0, correct?

Correct! And for your next question: you should always use radians; otherwise it is the angle*pi/180.