Working in spherical coordinates , and , where , , , select a volume element . There are six possible choices, namely,  times any one of the following:

, , , , ,  

Enter an integrand and the appropriate bounds of integration.

Compute the value of the integral either exactly or numerically.

Obtain a graph of the 3-D region determined by the limits of integration. The bounding faces for the region of integration are drawn with the following color-coding: .

Int, plot3d, plots[display]

Multivariate Calculus > Integration > Multiple Integration > Spherical

Student[MultivariateCalculus], VectorCalculus[int]