MATH 1920 Lecture Notes - Lecture 21: Cylindrical Coordinate System, Cartesian Coordinate System
16 Oct 2017
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16. 4 integration in polar, cylindrical, and spherical coordinates. In polar: 0 2 2and 0 8 29. *+ where r is the disk $, +&, = 4. This region is a rectangle in polar coordinates, but not in cartesian coordinates, so there must be a correction factor in the integral. If a region d in the xy-plane is given in polar coordinates by 81 8 8,, 2:(8) . Example: 2 = <=>28 gives a 4-leaved clover. V = {($,&,x):($,&) d,\:($,&) x \,($,&)} If d is given by 8: 8 8, , 2:(8) 2 2,(8), then: If d is nicer to express in polar coordinates, then use cylindrical coordinates. Example: let e be the region between the hemisphere x 1 = f1 $, &, $, +&, = x such that $ 0, & 0. $, +&, x 1 +f1 $, +&, D is given by: 0 8 t.
