In this example we use washer method to find volume of revolution around a horizontal axis.

In this example we use disk method to find volume of revolution around a vertical axis.

Sometimes you need to find the equation of the figure created by rotating a two-dimensional curve around an axis. More often you'll be asked to find the surface area or the volume of that figure, but if you need to find the equation that represents it, you can use the method in this video.

When you rotate a two-dimensional curve around a linear axis, it creates the outline of a three-dimensional object, for which you can find surface area using surface area of revolution formulas.

You can think about the arc length of a curve over an interval as the distance you'd have to walk from the point on the curve at the left edge of the interval to the point on the curve at the right edge of the interval.

Given two curves defined for y in terms of x, you can find the area in between them by taking the integral of the difference between the upper curve and the lower curve. Your first step will be to figure out which curve is higher and which curve is lower.

We'll use a tangent substitution in this example to simplify the integral.

We'll use a tangent substitution in this example to simplify the integral.

We'll use a sine substitution in this example to simplify the integral.

We'll use a sine substitution in this example to simplify the integral.