The final application of calculus within the polar coordinate system is calculating the area of surfaces of revolution formed by polar curves via integration. This includes surfaces of revolution formed by revolving polar curves around the polar axis (equivalent to the x-axis) and...

Another application of calculus within the polar coordinate system is the ability to calculate arc length of polar curves via integration. In the past we already saw how to calculate arc length of curves in the rectangular coordinate system in both rectangular form and parametric form. In fact,...

At the very beginning of Calculus 2, we learned how to find the area between two curves within the rectangular coordinate system by using integration. This process involved identifying a top and bottom curve for the area we wanted to find, as well as the two values of x that the area was...

In Calculus 1 you learn that the area under a curve can be calculated using a definite integral. Up to this point, those curves that we have been calculating the area beneath were rectangular curves within the rectangular coordinate system, either represented by rectangular equations, or more...

One of the first topics that you learn about in calculus is how to determine the slope of a tangent line at a particular point along a curve. This is known as "the tangent line problem" and we solve it with the concept of a derivative. We have used the derivative in the past to find slope of...

Graphing polar equations is similar to graphing rectangular equations, but is also different in many ways. There are very basic polar equations that represent the graphs of lines and circles which are also commonly represented by rectangular equations, but then are some special polar equations...

When working in the polar coordinate system rather than in the rectangular coordinate system, you will no longer be using rectangular equations in terms of x and y. Instead, you will be using brand new types of equations known as polar equations.

Similar to how rectangular equations in the form...

Up to this point in calculus and really every other math class you have probably taken, you have only been working within the rectangular coordinate system. This is the coordinate system in which you measure a horizontal distance (x) and a vertical distance (y) to create (x, y) coordinate...

Previously in Calculus 2 (Lesson 7), we looked at how to use definite integrals to calculate the area of surfaces of revolution, which are formed by revolving a curve around either the x-axis or y-axis. Whenever we calculated the area of these surfaces of revolution, we always...