show that an integral of the form

Question

∫00,a e^(-px) dx
is convergent if p>0 and divergent if p<0

Answer 1

∞
∫ e^-pxdx
a
=[-(1/p)e^-px] 0 to ∞
=(1/p)[1-e^(-px)]
=(1/p)(1-0) if p>0 since Lim e^(-px) =0 if p>0 and x->+∞
or
=undefined or divergent otherwise