?Integrating piecewise continuous functions Suppose f is continuous on the interval [a
Chapter 14, Problem 334(choose chapter or problem)
Integrating piecewise continuous functions Suppose f is continuous on the interval [a, c] and on the interval (c, b], where a < c < b, with a finite jump at x = c. Form a uniform partition on the interval [a, c] with n grid points and another uniform partition on the interval [c, b] with m grid points, where x = c is a grid point of both partitions. Write a Riemann sum for \(\int _a^b\ f(x)\ dx\) and separate it into two pieces for [a, c] and [c, b]. Explain why \(\int _a^b\ f(x)\ dx\ =\ \int _a^c\ f(x)\ dx\ +\ \int _c^b\ f(x)\ dx\).
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