Determine the convergence of ∫1∞sinxxpdx\int_1^{\infty} \frac{\sin x}{x^p} dx∫1∞xpsinxdx for p>0p > 0p>0.
Converges for all p>0p > 0p>0
Converges only if p>1p > 1p>1
Diverges for 0<p≤10 < p \le 10<p≤1
Converges only if p≥1p \ge 1p≥1