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.
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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)
