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For the following exercises, compute the center of mass $\overline{x} .$$$\rho=x^{3}+x e^{-x} \text { for } x \in(0,1)$$
$\overline{x}=\frac{4}{5}\left(\frac{11 e-25}{5 e-8}\right)$
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 6
Moments and Centers of Mass
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Okay, so we're asked to computer center of masculine. That p is equal. D'oh Thanks. U us. Thanks. Eat it. And in effect, okay. For ex contained in barrel to one. That's this X bar acquitted in the world from 01 of X times are a P which is therefore X four plus export heated in the X the X over to interval from Joe's one of this p which is excuse us Ex Agent X X is a popular you enjoy solving this yourself You get X four is equal to extra five over five. My speeds in the complex explained It's too exposed to over Mexico are four before my speech and little x X plus one Both the valet at once is all this gives me 11 You minus 25 over five e all over by You wanted space over or eat. Okay. It simplifies to for over five times 11 e minus 25 over five e minus eight
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