![Finding Areas using Definite Integration](http://4.bp.blogspot.com/-6gMqHGzt6C4/UOux5SNBSUI/AAAAAAAAOwY/OxOiQg3p22I/s400/lecture-find-areas-definite-integrate.png)
The area problem give us one of the interpretations of a definite integral that will lead us to the definition of the definite integral.
Let the Limit of n approaches to infinity (n → ∞)
Reviewing what you have learned in the topic Area Problem and the Riemann Sum series. As long as f is continuous the value of the limit is independent of the sample points xi used. If we let the Limit of n approaches to infinity (n → ∞). The definite integral of f from a to b is the define
![](http://2.bp.blogspot.com/-wdU8FYD1K-o/UN0OOj8wpPI/AAAAAAAAOYs/TUIG2QoNIK0/s400/limitdefintgrl.jpg)
provided the limit exists. The definite integral is defined to be exactly the limit and summation that we looked at in the previous topic to find the net area between a function and the x-axis.
Area Under a Curve
The area between the graph of y = f(x)and the x-axis is given by the definite integral below. This formula gives a positive result for a graph above the x-axis, and a negative result for a graph below the x-axis.
Note: If the graph of y = f(x) is partly above and partly below the x-axis, the formula given below generates the net area. That is, the area above the axis minus the area below the axis.
Formula: | |
Example 1: | Find the area between y = 7 – x2 and the x-axis between the values x = –1 and x = 2. |
Example 2: | Find the net area between y = sin x and the x-axis between the values x = 0 and x = 2π. |
Area Between a Curve
The area between curves is given by the formulas below.Formula 1: | |
for a region bounded above and below by | |
Formula 2: | |
for a region bounded left and right by | |
Example 1:1 | |
Example 2:1 | Find the area between |
Continue and apply what you have learned by answering some problems that you can find on this link Area Under a Curve and Between a Curve - Set 1 Problems.
credit: Bruce Simmons, Paul Dawkins (Lamar University)©2013 www.FroydWess.com Tags: Integral Calculus, Lectures
0 comments: Post Yours! Read Comment Policy ▼
PLEASE NOTE:
I have Zero Tolerance to Spam. It will be deleted immediately upon review.
Post a Comment