MATH 1920 Lecture 20: Triple Integrals (16.3)
15 Oct 2017
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Over boxes: r = [a, b] x [c, d] x [e, f] Fubini in 3d: (or we can change the. D is the projection of e onto the xy-plane. Z (integrate over lines parallel to the z-axis) Example: e is a tetrahedron with corners (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, Take ={(,):0 1,0 1 } (triangle expressed as vertically simple) Note: typically an iterated triple integral will look like: pt(u) pw(u) 0: treat x and y as constant initially, z is eliminated. Z where e is the solid region between c+c = and. C+c 4 (disk of radius 2 centered at origin) (d) Z: if (,) (,) on d then (,, if (,) on d then () (,) Properties: let d be a region in the xy-plane: the average of f(x,y) on d is.
