2) (From prob_5.doc) Find the total mass of the 3D object when the mass density rho and the object size is rho(r,phi,theta)=r^2sin(theta) where 1<r<2, 0<phi<pi and 0<theta<pi.
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The solution finds the mass of the given shape.
polar coordinates calculus
Use double integration in polar coordinates to find the volume of the solid that lies below the given surface and above the plane region R bounded by the given curve.
1. z=x^2+y^2; r=3
Evaluate the given integral by first converting to polar coordinates.
2. ∬_(0,x)^1,1▒〖x^2 dy dx〗
Solve by double integration in polar coordinates.
3. Find the volume of the solid bounded by the paraboloids z=12-2x^2-y^2 and
Find the centroid of the plane region bounded by the given curves. Assume that the density is δ≡1 for each region.
4. x=-2, x=2, y=0, y=x^2+1
Find the mass and centroid of the plane lamina with the indicated shape and
5. The region bounded by x=e, y=0, and y=lnx for 1≦x≦e,with