COPYRIGHT NOTICE
Copyright 2007 Samuel Dagan
dagan@post.tau.ac.il
/general/copyright.xhtml
Region excluding the origin
Integration with polar coordinates at a region,
not including the origin.
The origin of the figure is at (0,0)
©
Samuel Dagan
Region excluding the origin
φ
r
rmin(φ)
rmax(φ)
φmin
φmax
φmin∫
φmaxdφ
rmin
(φ)∫
rmax
(φ)f(r,φ)rdr
rmin
rmax
φmin(r)
φmax(r)
rmin∫
rmaxrdr
φmin(r)∫φmax(r)f(r,φ)dφ
x
y
The painted circle
represents a convex region
excluding the coordinates' origin.
The polar coordinates r
and φ
are used for integrating a function f(r,φ)
over the region.
The integration
over r
first and then over φ is formulated
and illustrated in the drawing.
The inverted order of integration is shown now.
The "next" button will remain active for
switching among both cases.
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