Question

set up the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines. y = 2 x , y = 2x

Answer 1

The volume of a solid of revolution using the method of disks can be found by integrating π [f(x)]^2 dx, where f(x) = 2x in this specific problem, over the interval of interest along the x-axis.

Step-by-step explanation:

The question involves using the method of disks or washers to find the volume of a solid of revolution. Since the curves given are identical (y = 2x, y = 2x), we need only one curve for this method. The integral can be set up as follows:

∫ π [f(x)]^2 dx, where f(x) = 2x and x varies from the lower to the upper bound of the region enclosed by the curve and the x-axis.

To rotate about the x-axis and find the volume V, we set up the integral as V = ∫ π (2x)^2 dx from a to b, where 'a' and 'b' are the x-coordinates of the points where the curve intersects the x-axis or any other specified limits.