With this next lesson in Calculus 2 we are going to take brief break from new advanced integration techniques and revisit limits from Calculus 1.

When we last looked at evaluating limits (Calculus 1 Lesson 7), we learned how to evaluate limits where x approached infinity. In most cases, these...

Rational functions are one of the most difficult types of functions to integrate. This is due to the variety of rational functions that exist and the fact that not all of them can be integrated in the same way. In the past we have been able to use a whole arsenal of techniques including...

In the previous lesson we focused on ways to solve trigonometric integrals that involved either sine and cosine, or secant and tangent. Now we can use those skills to help us with another advanced integration technique known as trigonometric substitution.

Often feared by many students due to its...

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...