Question

1 and 2 to using disk method 3 and for using washer method

Options:
A) Describe the disk and washer methods in calculus.
B) Apply differentiating techniques in calculus.
C) Define integration principles in calculus.
D) Explain the use of limits in calculus.

Answer 1

The disk and washer methods are techniques used in calculus to find the volume of solids revolution about an axis.

Step-by-step explanation:

The disk and washer methods are techniques used in calculus to find the volume of solids revolution about an axis.

The disk method involves integrating along the axis of rotation using disks or cylinders, while the washer method involves integrating along the axis of rotation using washers or annuli.

For example, if we have a region bounded by the curves y = f(x), y = g(x), x = a, and x = b, revolving around the x-axis, the volume using the disk method is given by the integral of (πf(x)^2 - πg(x)^2) dx, and the volume using the washer method is given by the integral of (π(f(x)^2 - g(x)^2)) dx.