Let R denote the region bounded by the curve y=x^3 and the lines x=0 and x=4. Find the volume generated when R is rotated 360 degrees about the x axis.

The area of a circle is given by (pi)r² and the area generated by R can be considered as an infinite number of circular areas.

Thus, we can write the area generated by R as the integral of (pi)(x³)² between x=0 and x=4.

The (indefinate) integral is: (pi)6x⁵

so the area is: (pi)6(4⁵-0⁵)=(pi)6(1024-0)

                                      =6144(pi)