diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index 8ac7fb1..6f2c40f 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -81,4 +81,8 @@ $$ \Delta x = \dfrac{1 - 0}{n} = \dfrac{1}{n}$$$$ x_i = 0 + \Delta xi + \dfrac{1 # Averages To find the average value of $f(x)$ on the interval $[a, b]$ is given by the formula: -Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ \ No newline at end of file +Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$ + +# The Fundamental Theorem of Calculus +Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then: +$$\int_a^b f(x) dx = F(b) - F(a)$$