Abstract
This chapter focuses on multiple integration of polar coordinates. While calculating the centroid of a plane region, it is necessary to assume that the region has a constant area density ρ. However, by using double integrals, one can get away from this restriction. When the centroid of a plane region is calculated, it is necessary to assume that the region has a constant area density ρ. However, by using double integrals, one can get away from this restriction. The density at any point on a semicircular plane lamina is proportional to the square of the distance from the point to the center of the circle. This double integral can be computed without using polar coordinates, but the computation is much more tedious. If f ≥ 0 on surface region S, then the triple integral ∫∫∫π∫(x,y,z) represents the volume in four-dimensional space ℝ4 of the region bounded above by f and below by S.
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