Integration in Physics: Applications & Area Under Curve

In summary, integral calculus is used in physics to calculate small forces, areas, or volumes over extended periods of time.
  • #1
Immanuel Can
18
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?
 
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  • #2
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.
 
  • #3
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.
 
  • #5
Try something basic: 2-d kinematics (acc. - vel. - displacement relationship)
 

What is integration in physics?

Integration in physics refers to a mathematical process of finding the area under a curve. It is used to calculate quantities such as displacement, velocity, and acceleration, among others. It is an essential tool in physics for solving problems involving continuous variables.

What are the applications of integration in physics?

Integration has various applications in physics, such as calculating the work done by a force, finding the net force on an object, determining the total energy of a system, and solving problems related to motion. It is also used in various fields of science, engineering, and economics.

How is integration used to calculate the area under a curve?

Integration is used to calculate the area under a curve by dividing the curve into small rectangles, calculating the area of each rectangle, and then summing up these areas to get an approximation of the total area under the curve. As the rectangles become smaller and the number of rectangles increases, the approximation becomes more accurate.

What is the difference between definite and indefinite integration?

Definite integration involves finding the area under a curve between specific limits, whereas indefinite integration involves finding the general solution to an integration problem without any given limits. In physics, definite integration is more commonly used as it provides a specific numerical value for the area under the curve.

How does integration relate to differentiation in physics?

Integration and differentiation are inverse operations. Integration is the reverse process of differentiation, and vice versa. In physics, differentiation is used to calculate instantaneous rates of change, while integration is used to calculate the cumulative effect or total change over a given time or distance.

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