Answer
$$\int^0_{-2}5^{-\theta}d\theta=\frac{24}{\ln5}$$
Work Step by Step
$$A=\int^0_{-2}5^{-\theta}d\theta$$
We set $-\theta=u$, which means $$-d\theta=du$$ $$d\theta=-du$$
- For $\theta=-2$, we have $u=2$ and for $\theta=0$, we have $u=0$
Therefore, $$A=-\int^{0}_{2}5^udu$$ $$A=-\frac{5^u}{\ln5}\Big]^{0}_{2}$$ $$A=-\frac{1}{\ln5}(5^{0}-5^2)$$ $$A=-\frac{1-25}{\ln5}$$ $$A=\frac{24}{\ln5}$$
