# Average value of function that converges?

I have a function $f$ that converges to a value:

$$f(x) = 1−s−A \beta ^ x$$ Where $A \in \mathcal{R}$, and $0< \beta <1$, $0< A <1$

I want to get the average value of for $x > r$. Since $\beta$ is a number between 0 and 1, I know the function converges. But I don't know how to calculate the integral :(

I would imagine it has something to do with: $$\int_r ^\infty 1−s− A \cdot \beta ^ x \partial x$$

But I have no clue on how to calculate this.

Any help?

Hint: $$\int a^x\,dx=\frac1{\ln a}a^x+C$$ What can you say about the convergence?