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Math Help - volume of solid revolution

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    volume of solid revolution

    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
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    Quote Originally Posted by sean123 View Post
    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 y= x^3, which is the same as [tex]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.
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