Learn why we get the area of a function by integrate it

Click For Summary
SUMMARY

The integration of a function provides the area under its curve, a fundamental concept in calculus. The discussion highlights a valuable tutorial available at this link, which effectively explains this concept. Additionally, it references an insightful article on Riemann and Lebesgue integration principles found at this resource. The emphasis is on the importance of understanding integration beyond mere application.

PREREQUISITES
  • Basic knowledge of calculus concepts, particularly integration
  • Familiarity with Riemann and Lebesgue integration
  • Understanding of mathematical functions and their graphical representations
  • Ability to interpret mathematical tutorials and educational resources
NEXT STEPS
  • Explore the tutorial on integration and area under a curve at this link
  • Study the principles of Riemann and Lebesgue integration through the article at this resource
  • Practice solving integration problems to solidify understanding of area calculation
  • Engage in discussions on calculus forums to clarify doubts and enhance comprehension
USEFUL FOR

Students, educators, and anyone interested in deepening their understanding of calculus, particularly those seeking to grasp the concept of integration and its applications in calculating areas under curves.

unseensoul
Messages
47
Reaction score
0
For those who want to understand why the integration of a function gives the area of it, you can take a look at...

http://www.mathsroom.co.uk/downloads/Integration-Area_Under_A_Curve.ppt"

I'm posting this because I think that not everyone who makes use of integration can really understand it. However, as it was very difficult to me to find such a good tutorial covering that aspect so well and clear, I am sharing it with those who are also interested in.
 
Last edited by a moderator:
Physics news on Phys.org

Similar threads

High School Integration from "Area Under Curve" Perspective: Explained
  • · Replies 11 ·
Replies
11
Views
2K
High School Calculating shaded area: I'm getting discrepancies between methods
  • · Replies 3 ·
Replies
3
Views
3K
High School Question about change of variables
  • · Replies 29 ·
Replies
29
Views
5K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad How to evaluate the enclosed area of this implicit curve?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Why is the integral of ##\arcsin(\sin(x))## so divisive?
  • · Replies 3 ·
Replies
3
Views
3K
High School Why don't we account for the constant in integration by parts?
  • · Replies 16 ·
Replies
16
Views
4K
High School Area under a sine integral graph
  • · Replies 8 ·
Replies
8
Views
3K
High School Why is the definite integral of 1/x from -1 to 1 undefined?
  • · Replies 4 ·
Replies
4
Views
7K
Undergrad The Basic Area Problem (introduction to the topic of integrals)
  • · Replies 24 ·
Replies
24
Views
4K