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lilisa27
 3 years ago
Integrate e^(2x) on the interval [1, 1]
lilisa27
 3 years ago
Integrate e^(2x) on the interval [1, 1]

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

ByteMe
 3 years ago
Best ResponseYou've already chosen the best response.0oops... there should be a factor of 1/2 outside of that second integral.....

lilisa27
 3 years ago
Best ResponseYou've already chosen the best response.0So the limits do change..... was curious about that.... So it should be.... 27.2899172?

ByteMe
 3 years ago
Best ResponseYou've already chosen the best response.0this 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.

lilisa27
 3 years ago
Best ResponseYou've already chosen the best response.0..... isn't u standing in for "2x".... therefore it would be e^4  e^(4)?

ByteMe
 3 years ago
Best ResponseYou've already chosen the best response.0yes 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

ByteMe
 3 years ago
Best ResponseYou've already chosen the best response.0if you wanted to back substitute so you could use x , then the limits would not change.

lilisa27
 3 years ago
Best 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....

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.0Fun fact: did you know you can actually perform definite integrals in scientific calculators?

swissgirl
 3 years ago
Best ResponseYou've already chosen the best response.0Yes someone like a half a yr ago informed me. Just cant remember who

lilisa27
 3 years ago
Best ResponseYou've already chosen the best response.0Uh, 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.

ByteMe
 3 years ago
Best ResponseYou've already chosen the best response.0Since 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.
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