# Math Help - Convergence of an integral

1. ## Convergence of an integral

Is the integral
1
∫sinx/x^sdx absolutely convergent if s<1 and divergent as s=1 and >1?
0

2. Originally Posted by miimi
Is the integral
1
∫sinx/x^sdx absolutely convergent if s<1 and divergent as s=1 and >1?
0
Well, $\sin(x)\underset{x\to 0}{\sim}x$. So your integral behaves like $\int_0^1\frac{dx}{x^{s-1}}$

3. So it is absolutely convergent if s<1, conditionally convergent if s=1 and divergent if s>1?