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 rec...

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 tang...

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 th...

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 points....

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 worked in terms of ...

Earlier in Calculus 2 (Lesson 6), we saw how to use a definite integral to calculate the arc length of a curve between two values of x. Up until now, we always calculated this arc length by working in terms of x because those curves had always been defined with functions in terms of x and y, or r...

In Calculus 1, we are introduced to the concept that a definite integral calculates the area under a curve between two values of x. Up to this point, the area that we wanted to calculate was beneath curves that were always defined with functions in terms of x and y, or rectangular equations. But ...

Another application of parametric derivatives is the ability to determine the concavity for plane/parametric curves. In fact, this is specifically an application of the second parametric derivative for a set of parametric equations.

You were first introduced to concavity in Calculus 1, where you...

One of the applications of parametric derivatives is the ability to determine the slope at a particular value of t (the parameter) along a plane/ parametric curve, and use that slope to find the equation of the tangent line for that value of t. This should be a familiar process, as finding slope ...