Question

Question content area top part 1: Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the x-axis: y=ex, y=0, x=0, and x=3.

A) 0 units3
B) π units3
C) π/2 units3
D) π2 units 3

Answer 1

The volume of the solid formed by rotating the region bounded by the curves around the x-axis is found using the formula V = π∫_{0}^{3} e2x dx. The correct answer isn't among the multiple-choice options because this integral doesn't yield a simple numerical value.

Step-by-step explanation:

The student is asked to find the volume of a solid generated by rotating the region bounded by the following curves about the x-axis: y=ex, y=0, x=0, and x=3. To find this volume, we use the method of disks or washers.

The formula for the volume of a solid of revolution using the disk method is V = π∫_{a}^{b} (radius)^2 dx, where the radius is the distance from the curve to the axis of rotation. For our problem, the radius is just y=ex and our limits of integration are from x=0 to x=3.

The correct formula for the volume of a solid is V = π∫_{0}^{3} e2x dx. After integrating, we find that this does not match any of the given multiple-choice options, indicating a potential error in the question or options presented. Volumes of solids of revolution are generally not integers and typically involve π and some exponential terms.