Question

Find the volume of the solid obtained by rotating the region enclosed by y = e^(4x) + 2, y = 0, x = 0, x = 1 about the x-axis using the method of disks or washers.

Answer 1

The volume of the solid formed by rotating the given region about the x-axis is found by integrating the square of the function defining the region's boundary, multiplied by pi, across the boundary limits.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region enclosed by y = e4x + 2, y = 0, x = 0, and x = 1 about the x-axis using the method of disks or washers, we can integrate across the bounds of x from 0 to 1.

The formula for the volume of a solid of revolution using the disk method is V = π ∫ab (radius)2 dx, where the radius is the function that defines the shape we are rotating, in this case y = e4x + 2.

The integral we need to solve is V = π ∫01 (e4x + 2)2 dx. After integrating, we get the volume of the solid.