Final answer:
The question involves calculating the volume of a region rotated about the x-axis using the disk method, where the radius of each disk is given by the function y = cos x, integrated from x = 0 to x = π/2.
Step-by-step explanation:
The student's question is about finding the volume of a region bounded by the curves y = cos x, y = 0, x = 0, and x = π/2 when rotated about the x-axis using the disk method. To accomplish this, we consider the region as a series of thin disks stacked along the x-axis, each with thickness dx, radius r(x) = cos x, and thus, area π [cos(x)]^2. The volume of each thin disk is then π [cos(x)]^2 dx, and we integrate this expression from x = 0 to x = π/2 to find the total volume of the solid of revolution:
- Set up the integral for the volume as V = ∫_{0}^{π/2} π [cos(x)]^2 dx.
- Evaluate the integral to find the volume of the solid.
This calculation uses the properties of a disk and the fact that all points on a rotating object trace circular paths.