Question

In a region bounded by y = cos x, y = 0, x = 0, and x = π/2, rotated about the x-axis, describe the resulting shape using the disk method.

Answer 1

The resulting shape can be described using the disk method by imagining slicing the region into infinitely thin disks perpendicular to the x-axis and integrating the volume formula from x = 0 to x = pi/2.

Step-by-step explanation:

The given region is bounded by the curves y = cos x, y = 0, x = 0, and x = pi/2. To describe the resulting shape using the disk method, we can imagine slicing the region into infinitely thin disks perpendicular to the x-axis. The radius of each disk is determined by the y-value of the curve y = cos x. The volume of each disk is given by the formula V = pi * r^2 * dx. By integrating this formula from x = 0 to x = pi/2, we can find the total volume and describe the resulting shape.