|Jul17-06, 09:05 PM||#1|
Mass problem...please check my work.
I don't know how to use LaTex or anything yet, so I'll just have to word this right.
Question: If the density of a fluid is given by
p = exp ^ -(x^2+y^2+z^2)^3/2
what is the total mass inside the unit sphere.
Since mass = integral (p dA)
where dA is the element of area
I switched to spherical coords...
M = [int(0..2*Pi)]:[int(0..Pi)]:[int(0..1) : [exp ^ -(p) ^ 3/2] * p^2*sin(phi) dp d(phi) d(theta)
where this is the triple integral of the function designated, with integration bounds listed in parantheses and the order of integration shown at the end of the equation.
I got the answer 2.213...if anyone sees any mistakes, please let me know. Sorry it's not easier to read...
|Jul17-06, 10:10 PM||#2|
What you use here actually is mass = the integral of p with respect to V, volume.
You did make a calculation error: in your integral for M, the expression for the mass should have a p2 term, not a p term, in the exponential (which will reduce to e-(p3))
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