## Volumes of Solids of Revolution (Disks, Washers, and Shells) [Video]

Finding the volume of the solid generated by rotating a bounded planar region about an axis of rotation is discussed. We cover the disk method, the washer method, and the method of cylindrical shells. We provide several examples of solids generated by revolving around both vertical and horizontal lines.

## Area Between Curves (The Best How to Guide) [Video]

If you already know the Fundamental Theorem of Calculus and find the area under a graph of a function, you are ready to find the area between curves. In this article, I’ll show you how to find the area of a region bounded by two curves. I’ll demonstrate both using vertical strips and horizontal strips.

## Taylor Polynomials and Approximations

By now, you’ve heard of the tangent line approximation. IN this article, I discuss polynomial approximations. I begin by motivating Maclaurin and Taylor and work through several examples.

## Taylor Series (and Maclaurin Series)

In this article, I introduce Taylor Series and Maclaurin Series, and then I discuss the convergence of Taylor Series. After that, I examine the Maclaurin series of the sine and cosine functions and consider precisely when the Maclaurin series for these functions converges.

## Convergence of Power Series (Differentiating and Integrating)

So now that you understand infinite series, it’s time to dive into power series. In this article, I explain what power series are and discuss the convergence of power series, including the radius of convergence. After that, I cover differentiating and integrating power series and finally combining power series.

## The Ratio Test and the Root Test

The Ratio and Root Tests are criterions for the convergence of an infinite series. I provide several examples using these convergence tests and several exercises.

## Alternating Series Test (and Conditional Convergence)

A series that alternates in sign is called alternating series. Under what conditions will an alternating series converge? Are there any conditions? Also, what does it mean to say or series is conditionally convergent? You will explore absolute and conditional convergence in this article.

## P-Series Test (Theory and Examples)

P-series is one of the most common types of series, and in this article, I go into detail. I explain what the p-series is and work through several examples on how to use the p-series test.

## Direct Comparison Test (and Limit Comparison Test)

One way to determine information about a series is to compare it to another series. This comparison is the idea behind the Direct Comparison Test. Then, I explain the Limit Comparison Test. You will also find many examples.

## Integral Test for Convergence (with Examples)

Yes, it’s possible to determine whether an infinite series is convergent using integration. I convince you that this is natural and that the Integral Test is valuable. You will also see several examples.