Linear Algebra For Dummies
Book image
Explore Book Buy On Amazon

You can use the Fundamental Theorem to calculate the area under a function (or just to do any old definite integral) that you integrate with the substitution method. What you want to do is to change the limits of integration and do the whole problem in terms of u. Say you want the area given by

image0.png
  1. Set u equal to x-squared.

  2. Take the derivative of u with respect to x.

    image1.png
  3. Solve for dx.

    image2.png
  4. Determine the new limits of integration.

    image3.png
  5. Make the substitutions, including the new limits of integration, and cancel the two 2xs.

    In this problem, only one of the limits is new because when x = 1, u = 1.

    image4.png
  6. Use the antiderivative and the Fundamental Theorem to get the desired area without making the switch back to x-squared.

    image5.png

About This Article

This article is from the book:

About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

This article can be found in the category: