Definite Integral: int[0,e] [e^(2x)] dx

[cmnalo]

∫e^(2x) dx Interval (0,e)

=ln│x│ + c Interval (0, e)

=ln│e│ - ln│0│

=ln│e│

I'm not sure if I'm doing this properly? I'm also not sure on how to reach the answer. I'm pretty sure ln│e│ = something but I can't find it in my book. Can any one explain?

The answer is : 1

 

[stapel]

You give "ln|x|" as the antiderivative of e^2x. Since x is non-negative, we don't need the absolute-value bars, so you really have "ln(x)". But:

. . . . .y = ln(x)

. . . . .y' = 1/x

...not e^2x. So this cannot be the correct integral.

Please reply showing all of your steps and reasoning. For instance, if you proceeded by u-substitution, then start from "u = 2x, so du = 2dx".

Thank you.

Eliz.