anonymous one year ago Find the area under the graph of f(x) = e-3ln(x) on the interval [1, 2].

1. jim_thompson5910

is the function $\LARGE f(x) = e^{-3\ln(x)}$ ??

2. anonymous

Yes

3. anonymous

Then what we're going to do is integrate the function from 1 to 2

4. freckles

you can make that function prettier before doing that whole integration thingy

5. jim_thompson5910

You can simplify things a bit first $\LARGE f(x) = e^{-3\ln(x)}$ $\LARGE f(x) = e^{\ln(x^{-3})}$ $\LARGE f(x) = x^{-3}$

6. anonymous

$\huge e^{-3\ln_e (x)} = e^{\ln_e(x^{-3})} = x^{-3}$ Does that make sense to you though?

7. anonymous

I got 0.375

8. anonymous

Yeah I understand how it's done.

9. anonymous

$\large \int_1^2 x^{-3}dx = \left.\frac{x^{-3+1}}{-3+1}\right]_{1}^2 = \left.\frac{x^{-2}}{-2}\right]_1^2=-\frac{1}{2}\left( \frac{1}{4} - 1\right) = \frac{3}{8} \qquad \checkmark$