] into n segments by x x x n ,..., such that ... , x i i − ∆ , i = , ,..., . For each i , , ,..., , the region in the xy -plane between the ordinates at x i and x i + ∆ which lies between the x -axis and the curve y ( ) can be approximated to an infinitesimal rectangle having area y i D , where y i i ( ) . When the plane region bounded by the curve ( ) , x -axis, and lines x and x is rotated by ° about x -axis, each of the infinitesimal rectangles at x x i also revolves and generates an elementary solid which is approximately a thin cylindrical disc with radius y i and height D x .
See Fig. . . The volume of the cylindrical disc at = − O Fig.
. h O Fig. . of - - x i is given by π y i ∆ , i , , ,..., .
Summing all these elementary volumes, we get the approximate volume of the solid of revolution as π y i i ∆