Home | 18.022 | Chapter 11 | Section 11.3

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Integrating over a sphere.

Suppose we have a sphere centered about r' of radius 2.

The integral of f (r) over it becomes

If we set g (r,, z) = f (x' + rcos, y' + rsin, z) we find that the same integral becomes, in cylindric coordinates

or with g (z' + sin,,cos) = h(,,) in spherical coordinates it becomes