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Integrals with e

  • #1

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

I thought maybe [itex]e^{1}[/itex] would just integrate like a normal function giving [itex]1/2e^{2}[/itex] 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?
 

Answers and Replies

  • #2
gb7nash
Homework Helper
805
1
This is a commonly known rule:

[tex]\int af(x) dx = a\int f(x) dx[/tex]

for constant a. Knowing this now...
 
  • #3
I don't understand how that rule applies exactly.
 
  • #4
gb7nash
Homework Helper
805
1
Think more about it. Is e1 a constant?
 
  • #5
Ok. I got it now. I wasn't thinking of [itex]e^{1}[/itex] as a constant. Thanks for the help.
 

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