Dirac delta function, sinx

Question

How to solve integration of del(sin x)dx The limits are from minus infinity to plus infinity. Please explain.

Answer 1

Using $$ δ(g(x))=\sum_{a:g(a)=0}\frac{\delta(x-a)}{|g'(a)|} $$ you would get $$ δ(\sin(x))=\sum_{k\in\Bbb Z} δ(x-k\pi). $$