If $r(t)$ represents the rate at which a country's debt is growing, then the increase in its debt between $2015$ and $2030$ is given by

$\frac{r(2030)-r(2015)}{2030-2015}$

$r(2030)-r(2015)$

$\frac{1}{15}{\displaystyle \underset{2015}{\overset{2030}{}}}{r}^{\text{'}}(t)dt$

$\frac{1}{15}{\displaystyle \underset{2015}{\overset{2030}{}}}r(t)dt$

${\displaystyle \underset{2015}{\overset{2030}{}}}r(t)dt$