Calculus 2: Volumes of Solids of Revolution

The first-quadrant area is bounded by the curve $y^2 = 4x$, the x axis, and the line x = 4 is rotated about the y axis. Find the volume generated: (a) By the ring method (b) By the shell method

Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis

$y = 2x^2$, $y = 0$, $x = 2$

Given $x^3 = y^5 + 2$, find the arc length from $y = 1$ to $y = 3$ and the surface area when the arc is rotated about the x-axis.

Calculate the volume of a solid of revolution by using the disc and shell methods for a given region in a plane spun about an axis.