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14.7 Day 2 Triple IntegralsUsing Spherical Coordinates
and more applications of cylindrical coordinates
This is a Klein bottle, It is a 4 dimensional objected depicted here in 3 dimensions
This object has only 1 side.
More information about the Klein bottle can be found at
http://www-maths.mcs.standrews.ac.uk/images/klein.html
Converting the differential(finding the Jacobian)
dxdydz=ρ sinφ dρdφdθ 2
Why? To find volume of the box at the left, use V=lwhV = dρ * ρdφ * rdθ(the r is from cylindrical coordinates)
From chapter 11r = ρsin φ
Hence dxdydz=ρ sinφ dρdφdθ
2
Problem 14 (spherical coordinates only)
Convert the integral from rectangular to spherical coordinates