volume of solid revolution

Feb 2010
8
0
Find the volume if the area bounded by the curve y=x^3, and the lines x=0 and y=8 when it is rotated with respect to the line x=5
 
Apr 2005
20,249
7,909
Find the volume if the area bounded by the curve y=x^3, and the lines x=0 and y=8 when it is rotated with respect to the line x=5
Since x= 5 is a vertical line, a point rotated around it will form a horizontal circle. A point on the line x= 0 forms a circle of radius 5 and a point on \(\displaystyle y= x^3\), which is the same as \(\displaystyle x= y^{1/3} forms a circle of radius 5- x= 5- y^{1/3}. What is the area of the region between those circles? Think of each as a thin disk of thicknes dy and "add" them all up.\)