diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 5296df9..8ac7fb1 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -72,8 +72,13 @@ $$ \Delta x = \dfrac{1 - 0}{n} = \dfrac{1}{n}$$$$ x_i = 0 + \Delta xi + \dfrac{1 7. $= \dfrac{5}{2}$ # Properties of Integrals -1. $\int_a^a f(x)dx = 0$ - An integral with a range of zero will always evaluate to zero. +1. $\int_a^a f(x)dx = 0$ - An integral with a domain of zero will always evaluate to zero. 2. $\int_b^a f(x)dx = -\int_a^b f(x) dx$ - The integral from $a \to b$ is equal to the integral from $-(b\to a)$ 3. $\int_a^b cf(x) dx = c \int_a^b f(x) dx$ - A constant from inside of an integral can be moved outside of an integral 4. $\int_a^b f(x) \pm g(x) dx = \int_a^b f(x) dx \pm \int_a^b g(x)dx$ - Integrals can be distributed -5. $\int_a^c f(x)dx = \int_a^b f(x)dx + \int_b^c f(x)dx$ - An integral can be split into two smaller integrals covering the same range, added together. \ No newline at end of file +5. $\int_a^c f(x)dx = \int_a^b f(x)dx + \int_b^c f(x)dx$ - An integral can be split into two smaller integrals covering the same domain, added together. + +# Averages +To find the average value of $f(x)$ on the interval $[a, b]$ is given by the formula: + +Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ \ No newline at end of file