• 3.2: Interpretations and Properties of Definite Integrals 

    • Definite integrals allow us to find the exact area underneath a curve. Without these integrals, it would be very difficult to even estimate the area under a curve that is not a linear function. The rules of integration allow us to find the area underneath any function.

      Subunit 3.2 focuses on finding definite integrals for various functions. The rules of integration learned in subunit 3.1 will be explored further as we work to find the exact values of integrals over a given region.

    • North Carolina School of Science and Mathematics: "Definite Integral Interpretation" Page

      Take notes as you watch the video. Listen to the presentation carefully until you are able to understand how to apply the rules of integration and then find the area of a specific region.


    • CK-12 Calculus: "Evaluating Definite Integrals"

      Read this material on evaluating definite integrals. This reading discusses the process of finding definite integrals and incorporates the rules of integrals to solve problems.
 Then, complete review questions 1-8 and 10 toward the bottom of the page. These exercises will provide you with the opportunity to find definite integrals using integration rules. The solutions to these problems are located here.


    • Khan Academy: "Definite Integrals" Page

      Take notes as you watch the videos. Listen to the presentations carefully until you are able to apply the rule of integrations to find a definite integral.


    • CK-12 Calculus: "Integration by Substitution"

      Complete review questions 2, 4, 6, and 10 toward the bottom of the page. These exercises will provide you with the opportunity to find definite integrals of various functions using the various integral rules. The solutions to these problems are located here.


    • CK-12 Calculus: "Integration by Substitution"

      Complete review questions 13-15 toward the bottom of the page. These exercises will provide you with the opportunity to find definite integrals of various functions using the various integral rules. The solutions to these problems are located here.


    • CK-12 Calculus: "Integration by Parts"

      Complete review questions 10-11 toward the bottom of the page. These exercises will provide you with the opportunity to find definite integrals of various functions using the various integral rules. The solutions to these problems are located here.


    • CK-12 Calculus: "Integration by Partial Fractions"

      Complete review questions 5-6 toward the bottom of the page. These exercises will provide you with the opportunity to find definite integrals of various functions using the various integral rules. The solutions to these problems are located here.