In this section, we will take a look at some applications of the definite integral. We will look how to use integrals to calculate volume, surface area, arc length, area between curves, average function value and other mathematical quantities. We will also explore applications of integration in physics and economics. Detailed solutions of the examples presented in the topics will help learn this math subject.

- Area of a Region Bounded by Curves
- Volume of a Solid with a Known Cross Section
- Volume of a Solid of Revolution: Disks and Washers
- Volume of a Solid of Revolution: Cylindrical Shells
- Area of a Surface of Revolution
- Average Value of a Function
- Probability Density Function
- Arc Length
- The Net Change Theorem
- Distance, Velocity and Acceleration
- Force, Work and Energy
- Fluid Pressure
- Mass and Density
- Center of Mass and Moments
- Moment of Inertia
- Pappus’s Theorem
- Integrals in Electric Circuits
- Applications of Integrals in Economics