I've been told by somebody (who is more advanced in math than me) that $ \int_0^{\infty}\!\sin(ax)\,dx = \frac{1}{a} $ But my basic intuition that the integral is the area under the curve $\sin(ax)$ makes me feel that it could have any value between $0$ and $1$. When questioned further she told me that one could do it by Laplace transforms. Although I don't exactly know what Laplace transforms are, or how they can be used to evaluate integrals, isn't my intuition more correct?
Thank you!