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Tagged with applications integration
4
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Volume vs. Surface Area Integrals
In order to find the volume of a sphere radiud $R$, one way is to slice it up into a stack of thin, concentric disks, perpendicular to the $z$-axis. a disk at any point $z$ will have radius $r=\sqrt{R^...
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Is the area independent of $n$? $ A=\int_0^\infty \frac{e^{-\frac{1}{tn}}(e^{-tn}(tn+1))}{t}~dt $
Consider the parametric equation $x=\frac{1}{t}e^{-tn}$ and $y=te^{-\frac{1}{tn}}.$ To integrate under this curve I put it in the proper form:
$$ A=\int_0^\infty \frac{e^{-\frac{1}{tn}}(e^{-tn}(tn+1))}...
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"Present value and accumulated value of money flow" problem
Find the present value and accumulated value after 10 years for an income stream with the rate of money flow $f(t) = 200 + 150t$ dollars per year and the rate of interest 12% compounded continuously. ...
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UNRESOLVED: Pushing oil out of a tank using work integration
I have a tank of oil with a density of $900\frac{kg}{m^3}$. My tank has a spout that is $2$ meters tall and the general radius of the tank is $6$ meters. It is half full of oil and I want to find the ...
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