Online Test Banks
Score higher
See Online Test Banks
eLearning
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

How to Split One Definite Integral into Two Definite Integrals

When solving area problems, you sometimes need to split an integral into two separate definite integrals. Here’s a simple but handy rule for doing this that looks complicated but is really very easy:

image0.png

This rule just says that you can split an area into two pieces and then add up the pieces to get the area that you started with.

image1.jpg

For example, the entire shaded area in the figure is represented by the following integral, which you can evaluate easily:

image2.png

Drawing a vertical line at

image3.png

and splitting this area into two separate regions results in two separate integrals:

image4.png

It should come as no great shock that the sum of these two smaller regions equals the entire area:

image5.png

Although this idea is ridiculously simple, splitting an integral into two or more integrals can be a powerful tool for solving a variety of area problems.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win $500. Easy.