Volumes of Revolution Around the x-axis
Introduction
You have used integration to find the area of a refion bounded by a curve, the x-axis and two vertical lines
⇒ You can derive this formula by considering the sum of an inifinte number of small strips of width 𝛿x. Each of these strips has a height of y, so the area of each strip is:
⇒ You can use a similar technique to find the volume of an object created by a rotating curve around a coordinate axis. If each of these strips is located through 2π radians (or 360 degrees) about the x-axis, it will form a shape that is approximately cylindrical
⇒ The volume of each cyclinder will be πy2𝛿x since will have a radius of y and height 𝛿x
Example
Extra
⇒ Also see our notes on: