Question

The region bounded by f(x) and g(x) is rotated about the x-axis. Find the volume of the resulting solid by any method.

a) Disk method
b) Washer method
c) Shell method
d) Integration method

Answer 1

To find the volume of the resulting solid when region is rotated around the x-axis, you can use the disk method, washer method, shell method, or integration method. All options are correct

Step-by-step explanation:

The volume of the resulting solid can be found using the disk method, washer method, shell method, or integration method. For the disk method, the volume is found by integrating the area of each disk formed by rotating the region around the x-axis. This can be calculated using the formula V = π ∫[f(x)]2 dx. For the washer method, the volume is found by subtracting the smaller disk formed by the region g(x) from the larger disk formed by the region f(x) when rotated around the x-axis.

The formula for this method is V = π ∫[(f(x))^2 - (g(x))^2] dx. The shell method involves integrating the product of the circumference of each shell formed by rotating the region and its height. The formula for this method is V = 2π ∫[x * (f(x) - g(x))] dx. Finally, the integration method involves using the given formula for the moment of inertia of a solid disk about the x-axis, which is MR².

All options are correct