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.
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.
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.
What is an infinite series, and how can you add up an endless amount of numbers and not get infinity? These are the questions I focus on in the article. First, I explain what an infinite series is and then discuss geometric series and the harmonic series. I also cover the divergence test and convergence rules.
Trigonometric substitution refers to an integration technique that uses trigonometric functions (mostly tangent, sine, and secant) to reduce an integrand to another expression so that one may utilize another known process of integration. I study these three primary forms and give examples to use complete the square to reduce one of these three methods.
I motivate an integration formula for finding the arc length of a smooth curve in a plane. Similarly, I use a formula for finding the surface area of the solid obtained by revolving a curve about an axis. After that, I demonstrate these formulas with several examples and provide exercises to develop integration skills.
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 method of cylindrical shells. We provide several examples of solids generated by revolving around both vertical and horizontal lines. Introduction to Solids of Revolution The solid … Read more
We explain, through several examples, how to find the area between curves (as a bounded region) using integration. We demonstrate both vertical and horizontal strips and provide several exercises. Introduction to Finding the Area Between Curves When applying the definition for the area between curves, finding the intersection points of the curves and sketching their … Read more