State whether the following integral is convergent or divergent:$$\int_{0}^{1} \frac{\sin(x)}{x^{1.5}} \ dx $$
The answer says that it converges due to a comparison with $\frac{1}{\sqrt{x}}$. I don't see how this works, as $\frac{1}{\sqrt{x}}$ is < $\frac{\sin(x)}{x^{1.5}}$ for $0 < x < 1$.
Any help will be greatly appreciated, thanks in advance.
