Section 4
Applications of Integration
By Boundless
![Thumbnail](../../../../../../figures.boundless-cdn.com/17655/raw/areabetweentwographs.jpg)
The area between the graphs of two functions is equal to the integral of a function,
![Thumbnail](../../../../../../figures.boundless-cdn.com/17656/square/volume-under-surface.jpg)
Volumes of complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17657/raw/gral-as-region-under-curve.jpg)
The average of a function
![Thumbnail](../../../../../../figures.boundless-cdn.com/17658/raw/shell-integration.jpg)
In the shell method, a function is rotated around an axis and modeled by an infinite number of cylindrical shells, all infinitely thin.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17647/square/ws2.gif)
Forces may do work on a system. Work done by a force (
![Thumbnail](../../../../../../figures.boundless-cdn.com/17648/square/rotationskoerper-animation.gif)
Disc and shell methods of integration can be used to find the volume of a solid produced by revolution.