Question Number 125876 by bramlexs22 last updated on 14/Dec/20
Commented by liberty last updated on 15/Dec/20
![W = Lim_(n→∞) Σ_(i = 1) ^n ρA(x_i ^∗ )Δx W = Lim_(n→∞) Σ_(i = 1) ^n 2,250π (x_i ^∗ )Δx = ∫_4 ^( 8) 2,250π (x) dx = 1,125π (x^2 )]_4 ^8 = 1,125π × 48 = 169,646 lb−ft](https://www.tinkutara.com/question/Q125877.png)
$${W}\:=\:\underset{{n}\rightarrow\infty} {\mathrm{Lim}}\:\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\rho{A}\left({x}_{{i}} ^{\ast} \right)\Delta{x}\:\:\:\:\:\:\: \\ $$$${W}\:=\:\underset{{n}\rightarrow\infty} {\mathrm{Lim}}\:\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{2},\mathrm{250}\pi\:\left({x}_{{i}} ^{\ast} \right)\Delta{x} \\ $$$$\left.\:\:\:\:\:=\:\int_{\mathrm{4}} ^{\:\mathrm{8}} \mathrm{2},\mathrm{250}\pi\:\left({x}\right)\:{dx}\:=\:\mathrm{1},\mathrm{125}\pi\:\left({x}^{\mathrm{2}} \right)\right]_{\mathrm{4}} ^{\mathrm{8}} \\ $$$$\:\:\:\:\:=\:\mathrm{1},\mathrm{125}\pi\:×\:\mathrm{48}\:=\:\mathrm{169},\mathrm{646}\:{lb}−{ft} \\ $$$$ \\ $$