A common type of integral that you will encounter in calculus is a trigonometric integral containing multiple trig functions. When these integrals are of a certain form, either containing both sin(x) and cos(x), or tan(x) and sec(x), there are techniques that can be used to make them possible to...

When solving integrals that require integration by parts, you may encounter some integrals that require the use of the integration by parts process multiple times in order to be completely solved. This can quickly become a tedious process that is fairly time consuming, not to mention that there...

The next major group of concepts we will look at in Calculus 2 after the applications of integrals is advanced integration techniques. The first of those techniques we are going to focus on is known as Integration By Parts.

Integration By Parts will allow us to solve integrals that we previously...

The final application of definite integrals that we encounter in Calculus 2 is the ability to find the fluid force on a vertically submerged surface. 

If you've ever been swimming in a pool, river, ocean, or any other body of water, you've probably noticed that when you try to submerge...

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...

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...

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...

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...

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...