Proposition 7.1.12: Properties of the Riemann Integral
Suppose f and g are Riemann integrable functions
defined on [a, b]. Then
- c f(x) + d g(x) dx = c f(x) dx + d g(x) dx
- If a < c < b then f(x) dx = f(x) dx + f(x) dx
- | f(x) dx | | f(x) | dx
- If g is another function defined on [a, b] such that g(x) < f(x) on [a, b], then g(x) dx f(x) dx
- If g is another Riemann integrable function on [a, b] then f(x) . g(x) is integrable on [a, b]