Calculating Mass Inside a Unit Sphere using Spherical Coordinates

[62646264]

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...

 

[0rthodontist]

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))