The given area bounded by y= x3 +1, the x-axis, x=0 and x=3 is shown in the figure given below, shaded in red color. This is rotated around x axis. Consider an elementary circular disc formed by rotation of element of length y and width dx, as shown in blue in the figure. The volume of this disc will be πy2 dx . The volume of the solid formed by rotation of the whole area, would be
Substituting for y= x3+1, the volume of the solid
will be equal to 
On simplifying we
will have 
.Solving
the definite
integral it will be 
Or 
Or 
cubic units.
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