# Delta function (hard question)

## Homework Statement

Compute ∫$^{∞}_{-∞}$dx (x2+a2)-1δ(sin(2x)), without calculating the resulting sum.

## Homework Equations

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

## The Attempt at a Solution

Does anyone know this integral ? I haven't seen before any similar examples.

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vanhees71
$$\delta[f(x)]=\sum_{k} \frac{1}{\left |f'(x_k) \right|} \delta(x-x_k),$$
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 $k$.