The Area Under a Curve: approximating the definite integral
3358 views
|
1
rating
Lesson Summary:
This lesson teaches how to find the area under a curve by approximating the integral of a function. The instructor uses the example of the area between y = x^2 and y = 0 from x = 1 to x = 3, using four rectangles to approximate the area. The formula for the area is approximately f1 times delta x plus f2 times delta x plus f, et cetera, and you can calculate the area of each rectangle with it. With this method, you can only have four rectangles, so the area is always an approximation, but it's a good starting point.
Lesson Description:
How to find the area under a curve by approximating the integral of a function.
Produced by Kent Murdick
Instructor of Mathematics
University of South Alabama
Questions answered by this video:
- How do you find the area under a curve?
- How do you approximate the area under a curve?
- How can you use rectangles to find the area under a curve?
-
Staff Review
This video does a great job of explaining the way to approximate the area under a curve using rectangles. A must-see for understanding the idea of an integral and as a precursor to understanding the Fundamental Theorem of Calculus.
