# Homework Help: Delta function (hard question)

1. Sep 2, 2013

### helpcometk

1. The problem statement, all variables and given/known data
Compute ∫$^{∞}_{-∞}$dx (x2+a2)-1δ(sin(2x)), without calculating the resulting sum.

2. Relevant equations

This is a very specific integral which ,has a delta function δ operating on sin function

3. The attempt at a solution
Does anyone know this integral ? I haven't seen before any similar examples.

2. Sep 2, 2013

### vanhees71

You haven't listed all relevant equations yet:
$$\delta[f(x)]=\sum_{k} \frac{1}{\left |f'(x_k) \right|} \delta(x-x_k),$$
where $x_k$ runs over all zeros of $f$, which all must be simple zeros of course in order that $f'(x_k) \neq 0$ for all $k$.