Solving Integrals with e: Homework Equations & Solutions

[dlthompson81]

Homework Statement

\begin{equation} \int_{-1}^{1} e^{u+1} \end{equation}

Homework Equations

The Attempt at a Solution

I really seem to struggle with any problems with e in them. I think I may have missed some of the basic rules or something, but I can't seem to find what I missed.

My guess on this one would be to rewrite the equation into:

\begin{equation}\int_{-1}^{1} e^{u} e^{1}\end{equation}

I know that the integral of $e^{u}$ is $e^{u}$ but I don't know how to integrate $e^{1}$. I'm not even sure if I rewrote the problem correctly. I know that the answer is $e^{2}-1$ but I can't seem to figure out how to get there.

I thought maybe $e^{1}$ would just integrate like a normal function giving $1/2e^{2}$ but I couldn't get it to work out with that either.

I'm totally lost with these e functions. What am I doing wrong?

 

[gb7nash]

This is a commonly known rule:

$$\int af(x) dx = a\int f(x) dx$$

for constant a. Knowing this now...

 

[dlthompson81]

I don't understand how that rule applies exactly.

 

[gb7nash]

Think more about it. Is e¹ a constant?

 

[dlthompson81]

Ok. I got it now. I wasn't thinking of $e^{1}$ as a constant. Thanks for the help.