Final answer:
To find the volume of the solid obtained by rotating the region bounded by the curves y = 3 sin(x) and y = 3 cos(x) about the line y = 3 sin(x), we can use the method of cylindrical shells. The volume is 6π cubic units.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the curves y = 3 sin(x) and y = 3 cos(x) about the line y = 3 sin(x), we can use the method of cylindrical shells.
The radius of each cylindrical shell is the distance from the line of rotation to the curve, which is y = 3 sin(x). The height of each cylindrical shell is the difference between the two curves at a given x-value, which is 3 sin(x) - 3 cos(x).
Integrating the volume of each cylindrical shell from x = 0 to x = 2π will give us the total volume of the solid.
The volume of the solid obtained by rotating the region bounded by the curves y = 3 sin(x) and y = 3 cos(x) about the line y = 3 sin(x) is 6π cubic units.