Show that for all natural integer $p$, the integral $$I _ { p } = \int _ { - \infty } ^ { + \infty } e ^ { - ( t - p \pi ) ^ { 2 } } \sin t \mathrm {~d} t$$ is absolutely convergent and that it equals zero.
Show that for all natural integer $p$, the integral
$$I _ { p } = \int _ { - \infty } ^ { + \infty } e ^ { - ( t - p \pi ) ^ { 2 } } \sin t \mathrm {~d} t$$
is absolutely convergent and that it equals zero.