Determine the convergence of the integral ∫1∞sin(x)xpdx\int_1^{\infty} \frac{\sin(x)}{x^p} dx∫1∞xpsin(x)dx for p>0p > 0p>0.
Converges for all p>0p > 0p>0
Converges only for p>1p > 1p>1
Diverges for all p>0p > 0p>0
Converges for p>0p > 0p>0 by the Dirichlet Test