Integrating piecewise continuous functions Suppose f is
Chapter 5, Problem 76(choose chapter or problem)
Integrating piecewise continuous functions Suppose f is continuous on the intervals 3a, p4 and 1p, b4, where a 6 p 6 b, with a finite jump at p. Form a uniform partition on the interval 3a, p4 with n grid points and another uniform partition on the interval 3p, b4 with m grid points, where p is a grid point of both partitions. Write a Riemann sum for 1 b a f 1x2 dx and separate it into two pieces for 3a, p4 and 3p, b4. Explain why 1 b a f 1x2 dx = 1 p a f 1x2 dx + 1 b p f 1x2 dx.
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