Determine if a improper integral converge using some criterion

Question

There is a criterion to decide if the following integral converge or not?

$$\displaystyle\int_0^\infty \left(\dfrac12\right)^x\sin x\,dx$$

The idea is to avoid calculating its value.

Answer 1

hint

$$|(\frac 12)^x\sin(x)|\le e^{-x\ln(2)}$$

By comparison test, the integral is absolutely convergent.