Integration in Physics: Applications & Area Under Curve

  • Context: High School 
  • Thread starter Thread starter Immanuel Can
  • Start date Start date
  • Tags Tags
    Integration Physics
Click For Summary

Discussion Overview

The discussion revolves around the applications of integration in physics, particularly focusing on the concept of finding the area under a curve and its relevance in various physical contexts. Participants explore theoretical and practical implications of integration in understanding physical systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses curiosity about the applications of integration in physics, particularly regarding the area under a curve.
  • Another participant suggests that integration is fundamental to various applications, including calculating forces by integrating over volumes, as illustrated by the example of the force acting on Earth due to the Sun.
  • A different participant mentions that integration can account for the historical states of a system, indicating that current states depend on past conditions.
  • Additional applications discussed include calculating total amounts of physical quantities from local distributions and the use of transforms like Fourier, Hilbert, and Laplace.
  • One participant recommends exploring basic concepts in 2-dimensional kinematics related to acceleration, velocity, and displacement relationships.

Areas of Agreement / Disagreement

Participants present a variety of applications and perspectives on integration, with no consensus on a singular application or approach, indicating multiple competing views remain in the discussion.

Contextual Notes

Some participants reference specific physical concepts and mathematical techniques without fully resolving the implications or dependencies of these applications on underlying assumptions or definitions.

Immanuel Can
Messages
18
Reaction score
0
I've just started integral calc and I'm just curious as to the application of integration in physics. Being a new physics major(started this summer), this is something I have not yet encountered. What is finding the area under a curve used for?
 
Physics news on Phys.org
Everything.

Generalize the idea to a volume, in other words summing up stuff over 3-dimensions (because 1-dimensional stuff is kinda boring). Imagine, for example, you want to figure out the force acting on the Earth due to the Sun. Well, you figure out the infinitesimal force caused by a infinitesimal volume of the Sun a certain distance away from the Earth. Then you do it for another piece of the Sun at another distance away from the Earth. You can do that for every little piece of the Sun. However, you want to find the whole force due to the entire Sun. Well, you integrate over the volume of the Sun and that tells you the force due to the Sun on the Earth.
 
Immanuel Can said:
I've just started integral calc and I'm just curious as to the application of integration in physics. Being a new physics major(started this summer), this is something I have not yet encountered. What is finding the area under a curve used for?

Another application is accounting for the past history of a system. In many applications, the current state of an object (stress, polarization, temperature, etc) is dependent on what happened to the object in the past.

Other applications include calculating a total amount of something (angular momentum, electric field, salt, etc) given a local distribution of the components; certain classes of transforms (Fourier, Hilbert, Laplace, etc) that relate different properties; etc.
 
Try something basic: 2-d kinematics (acc. - vel. - displacement relationship)
 

Similar threads

Graduate Unsolved Problems in Near Surface Geophysics
  • · Replies 4 ·
Replies
4
Views
3K
High School Question about units for "area under curve"
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad What exactly does integration signify?
  • · Replies 6 ·
Replies
6
Views
3K
Calculate the area of this pond with functions given for the perimeter
  • · Replies 2 ·
Replies
2
Views
997
Graduate How do people explore new ideas in physics?
  • · Replies 52 ·
2
Replies
52
Views
4K
High School Explain Integration to me, please
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Using AI to evaluate white papers?
  • · Replies 42 ·
2
Replies
42
Views
3K
High School Integration from "Area Under Curve" Perspective: Explained
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Area under the curve of a temperature-time graph -> energy?
  • · Replies 10 ·
Replies
10
Views
5K
Undergrad Pure Physicist - A physics simulator app
  • · Replies 3 ·
Replies
3
Views
4K