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ByteMeBest ResponseYou've already chosen the best response.0
let u=2x so du=2dx or \(\large \frac{1}{2}du=dx \) so, \(\large \int_{1}^{1}e^{2x}dx=\int_{2}^{2}e^udu=e^u_{2}^{2}= \) ???
 one year ago

ByteMeBest ResponseYou've already chosen the best response.0
oops... there should be a factor of 1/2 outside of that second integral.....
 one year ago

lilisa27Best ResponseYou've already chosen the best response.0
So the limits do change..... was curious about that.... So it should be.... 27.2899172?
 one year ago

ByteMeBest ResponseYou've already chosen the best response.0
this is what it should look like: \(\large \int_{1}^{1}e^{2x}dx=\frac{1}{2}\int_{2}^{2}e^udu=\frac{1}{2}e^u_{2}^{2}=\frac{1}{2}(e^2e^{2})=\frac{1}{2}(\frac{e^41}{e^2})=\frac{e^41}{2e^2} \) that's the exact form.
 one year ago

lilisa27Best ResponseYou've already chosen the best response.0
..... isn't u standing in for "2x".... therefore it would be e^4  e^(4)?
 one year ago

ByteMeBest ResponseYou've already chosen the best response.0
yes it is but we made a usubstitution that enables us to evaluate the integral in terms of u so we use 2 and 2 as the lower/upper limits of integration
 one year ago

ByteMeBest ResponseYou've already chosen the best response.0
if you wanted to back substitute so you could use x , then the limits would not change.
 one year ago

lilisa27Best ResponseYou've already chosen the best response.0
....Pretty sure in class, even when making u substitutions, we always would convert back to x form after integrating, keeping the new limits of the integral, and substituting those numbers in for x....
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
Fun fact: did you know you can actually perform definite integrals in scientific calculators?
 one year ago

swissgirlBest ResponseYou've already chosen the best response.0
Yes someone like a half a yr ago informed me. Just cant remember who
 one year ago

lilisa27Best ResponseYou've already chosen the best response.0
Uh, yeah.... but when I do it by hand I'm not getting the right answer. And I have to show my work as though I did it by hand.
 one year ago

ByteMeBest ResponseYou've already chosen the best response.0
Since this is a definite integral, the answer is numeric. so i don't see why you would back substitute back to x if we already made the transition from x to u. But either way, the numeric answer should be the same if you did a back subsitution to x or used the new limits involving u.
 one year ago
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