Describe the rules for working with definite integrals (Table 5.6). Give examples.

TABLE 5.6 Rules satisfied by definite integrals f" f(x) dx = -f" f(x) dx 1. Order of Integration: 2. Zero Width Interval: 3. Constant Multiple: 4. Sum and Difference: 5. Additivity: 6. Max-Min Inequality: 7. Domination: ["F(x) f(x) dx = 0 b kf(x) dx = k f*f Skf(x) S (PC) S ["Harde [arde - [ Hards + S (f(x) = g(x)) dx = f(x) dx + f(x) dx = f(x) dx f(x) dx b = [ f(x) dx = a min f.(b-a) - Sf(x) f(x) dx = f(x) dx = max f (b a). A definition If f has maximum value max f and minimum value min fon [a, b], then A definition when f(a) exists f(x) = g(x) on [a, b] [ f(x) Any constant k g(x) dx ) dx = [1 g(x) dx .b. f(x) = 0 on [a, b] [ f(x f(x) dx = 0 (Special case)