0
$\begingroup$

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?

$\endgroup$

1 Answer 1

0
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.