Applying Properties of Definite Integrals

#6.6 Applying Properties of Definite Integrals

Welcome back to AP Calculus! In this guide, we will be focusing on different definite integral properties and how to use various known integrals to determine an unknown definite integral. Although this may seem complicated at first, once you memorize the properties you will be able to answer any question that has to do with this topic!

#💭 What is a Definite Integral?

Integrating a given function over the give interval $[a,b]$ to get a value (an actual number, rather than the integration + c) as a final answer. Another way to think about this is that you are finding the area of under $f(x)$ on $[a,b]$.

$$\int_{a}^{b}f(x), dx$$

It is important to recognize what each of the terms above mean, so here is a quick summary!

• The $b$ is the upper limit of integration, so it will always be the larger number in the given interval.
• The $a$ is the lower limit of integration, so it will be the smaller number in the given interval.
• $f(x)$ is the function that are integration with respect to x. !area-under-graph-function-definite-600nw-2381272671.webp

A curve where the area under the curve from a to b is shaded into to define a definite integral.

Image Courtesy of Shutterstock

#📝 Definite Integral Properties

Here are the properties that should both be understood and memorized.

1. The Zero Rule: When the upper ...