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anonymous
 one year ago
Find the area under the graph of f(x) = e3ln(x) on the interval [1, 2].
anonymous
 one year ago
Find the area under the graph of f(x) = e3ln(x) on the interval [1, 2].

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1is the function \[\LARGE f(x) = e^{3\ln(x)}\] ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then what we're going to do is integrate the function from 1 to 2

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you can make that function prettier before doing that whole integration thingy

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1You can simplify things a bit first \[\LARGE f(x) = e^{3\ln(x)}\] \[\LARGE f(x) = e^{\ln(x^{3})}\] \[\LARGE f(x) = x^{3}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge e^{3\ln_e (x)} = e^{\ln_e(x^{3})} = x^{3} \] Does that make sense to you though?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I understand how it's done.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large \int_1^2 x^{3}dx = \left.\frac{x^{3+1}}{3+1}\right]_{1}^2 = \left.\frac{x^{2}}{2}\right]_1^2=\frac{1}{2}\left( \frac{1}{4}  1\right) = \frac{3}{8} \qquad \checkmark\]
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