?Properties of integrals Suppose that \(f(x)\ \geq\ 0\) on [0, 2], \(f(x)\ \leq\ 0\) on

Chapter 14, Problem 332

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Properties of integrals  Suppose that \(f(x)\ \geq\ 0\) on [0, 2], \(f(x)\ \leq\ 0\) on [2, 5], \(\int _0^2\ f(x)\ dx=6\), and \(\int _2^5\ f(x)\ dx=-8\). Evaluate the following integrals.

a. \(\int _0^5\ f(x)\ dx\)                                         b. \(\int _0^5\ |f(x)|\ dx\)

c. \(\int _2 ^5\ 4|f(x)|\ dx\)                                          d. \(\int _0^5\ (f(x)+|f(x)|)\ dx\)

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