From 5e76ded24117eea028df284f0fbf750db571f05f Mon Sep 17 00:00:00 2001 From: arc Date: Tue, 25 Mar 2025 10:11:37 -0600 Subject: [PATCH] vault backup: 2025-03-25 10:11:37 --- education/math/MATH1210 (calc 1)/Integrals.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index e68ab66..4110345 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -53,6 +53,10 @@ $$ \int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i = 1}^n f(x_i)\Delta x$$ $f(x_i)$ is the *height* of each sub-interval, and $\Delta x$ is the change in the *x* interval, so $f(x_i) \Delta x$ is solving for the area of each sub-interval. +- If your function is always positive, then the value of a definite integral is the area under the curve. +- If the function is always negative, then the value of a definite integral is the area above the curve to zero. +- If the function has both positive and negative values, the output is equal to the area above the curve minus the area below the curve. + ## Examples > Find the exact value of the integral $\int_0^1 5x \space dx$