I am looking for a function $f$ with the following properties:

- $f$ is continuous on $[0,\infty[$
- $f(0)=1$
- $f(x)\to0$ as $x\to\infty$
- $\int_0^{\infty} f(x) \,\mathrm{d}x = \infty$

It is not difficult to find a such a function, for example $f(x) = 1/(x+1)$ would do it. However, I am looking for an example where I can "proof" that the area under the curve (i.e. $\int_0^{\infty} f(x) \,\mathrm{d}x $) goes to infinity for $x \to \infty$ for an audience which doesn't know of how to integrate or differentiate functions.

So a "visual" proof would be sufficient too.