Another application of definite integrals is the ability to find the center of mass for planar lamina, or thin pieces of material with a negligible thickness. However, before we can look at the calculus of finding the center of mass for these planar lamina, we need to discuss what a center of mas...

The next application for definite integrals that we are going to look at deals with the concept of work from physics. Simply put, work is the energy transferred to or from an object when it is moved by a force.

The most simple case of work is work done by a constant force, or a force that is not...

In previous lessons we learned how to find the volume of solids of revolution using definite integrals via the disk, washer, and shell methods. Similarly, we can determine the area of surfaces of revolution using definite integrals.

But what is a surface of revolution? Well they are similar to s...

Another application of definite integrals is the ability to find the arc length of curves. In algebra you learn how to find the distance between two points, or the length of a line segment using the distance formula, but this can be extended using calculus to find the length of curves.

The formu...

Previously we have seen how to use the the disk method (among other methods) to calculate the volume of solids of revolution with definite integrals. However, we are not limited to calculating the volume of solids of revolution, or solids with circular cross sections. We can also use definite int...

So far we have seen how to use definite integrals to calculate the volume of solids of revolution with the disk and washer method. However, they are not the only methods that can be used to calculate that volume. There is an alternative method. Instead of using thin disks or thin washers to repre...

Previously we looked at how to use the disk method, which allowed us to use definite integrals to calculate the volume of solids of revolution. However, all of the solids we looked at so far were complete solids. But what if we had a solid of revolution that featured a hole?

To do this, we use a...

Another application of definite integrals is the ability to calculate the volume of solids with known cross sections. The first type of solid we will look at is a solid of revolution, or a solid with circular cross sections.

Solids of revolution are formed by revolving an enclosed region around ...

In Calculus 1 you learn that the definite integral can be used to calculate the area of a region beneath a curve. However, what if we wanted to calculate the area of a region that is between two curves? It turns out, that we can also use a definite integral to calculate this area, as long as well...