How Do You Evaluate the Integral of e^x from 0 to 3 ln2?

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Homework Statement



Evaluate

∫ e^x dx

upper limit: 3 ln2
lower limit: 0



Homework Equations





The Attempt at a Solution




I'm not sure if I'm doing this right;

the integral of e^x = e^x

now with the lmits

[e^3ln2 - e^0]

?

lol thanks
 
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yup. now all you need to do is just simplify with your natural log and exponential rules.
 
I understand it now.

e^3ln2 = e^ln8 = 8

e^0 = 1

8-1 = 7Thanks
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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