Integration in Physics: Applications & Area Under Curve

[Immanuel Can]

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?

 

[Pengwuino]

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.

 

[Andy Resnick]

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.

 

[Naty1]

You can skim here in Wikipedia for some ideas:

http://en.wikipedia.org/wiki/Maxwell's_equations#Units_and_summary_of_equations

and follow the "SEE ALSO" links near the bottom of the page.

 

[SteamKing]

Try something basic: 2-d kinematics (acc. - vel. - displacement relationship)