\[\int_{a}^{b} f(x)dx = [F(x)]_{a}^{b} = F(b) - F(a) \]

\[ \frac{d}{dx}F(x) = f(x) \]

Find the average value for a function f(x) on some interval: \[Average = \frac{\int_{a}^{b }f(x)dx}{b-a} \]

• Essence of Calculus