In taking antiderivatives of monomials of the form x ^ n, the candidate solution using Cavalieri's quadrature formula would be \ tfrac { 1 } { n + 1 } x ^ { n + 1 } + C . This candidate solution is in fact correct except when n =-1.
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The most obvious example is when D is a circular disk : here " k " = 1, " z " 1 is the center of the circle, and " c " 1 equals the area of D . That quadrature formula expresses the mean value property of harmonic functions with respect to disks.
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