Integrating Graphs with Two Intervals: How to Find the Mean?

In summary, if a function f(x) is equal to a constant k only within two intervals a < x < b and c < x < d, finding the integral of the function is easy by adding the integrals over each interval. The mean value of the function over the two intervals can be found by dividing the integral by the combined length of the intervals. Additionally, if the function is zero everywhere else, the integral can be evaluated as 0 outside the two intervals.
  • #1
Dollydaggerxo
62
0
In general,
if f(x)=k but only for a < x < b and c < x < d
how would you integrate the graph ?
To find the mean for example, would you find the mean for each and add together, or is there some special thing for this case?
 
Mathematics news on Phys.org
  • #2
What's the value of f(x) for x not in the two intervals? Presumably the value is zero, but you didn't state this.

Assuming for the moment that f(x) = 0 outside the two intervals, finding the integral of this function (not the integral of its graph) is easy to find.
[tex]\int_{-\infty}^{\infty} f(x) dx~=~\int_a^b f(x) dx~+~\int_c^d f(x) dx~=~k(b - a)+ k(d - c)[/tex]

To find the mean value of this function over the two intervals, evaluate the integral of the function (see above), and then divide by the length of the two intervals, b - a + d - c.
 
  • #3
sorry, yes I meant if it is zero everywhere else.
Thanks
 

1. What is a graph with two intervals?

A graph with two intervals is a type of graph that represents data in two separate intervals or ranges. These intervals can be represented on the x-axis, y-axis, or both. It is commonly used to compare and analyze data that falls into two distinct categories or time periods.

2. How do you interpret a graph with two intervals?

To interpret a graph with two intervals, you should first identify the two intervals being represented. Then, look at the data points within each interval and note any trends or patterns. Compare the data points in each interval to see if there are any significant differences or similarities.

3. What types of data are best represented by a graph with two intervals?

A graph with two intervals is best suited for representing data that can be divided into two distinct categories or time periods. For example, it can be used to compare data from two different years, two different groups, or two different variables.

4. How do you create a graph with two intervals?

To create a graph with two intervals, you will need to first determine the type of graph that is most appropriate for your data (e.g. bar graph, line graph, scatter plot). Then, you can plot the data points for each interval on the graph, labeling the intervals on the appropriate axis. Make sure to use different colors or patterns to differentiate between the two intervals.

5. What are the benefits of using a graph with two intervals?

Using a graph with two intervals allows for easy comparison and analysis of data that falls into two distinct categories or time periods. It can help identify trends, patterns, and differences between the two intervals, making it a valuable tool for decision-making and problem-solving in various fields such as economics, science, and social sciences.

Similar threads

Replies
7
Views
941
Replies
7
Views
2K
  • General Math
Replies
2
Views
852
Replies
5
Views
1K
Replies
1
Views
902
Replies
4
Views
284
  • General Math
Replies
9
Views
2K
  • General Math
Replies
21
Views
1K
Replies
76
Views
4K
  • General Math
Replies
6
Views
2K
Back
Top