math

Finf the volume of the solid generated by revolving the region bounded by the curve. x=2/(y+1), x=0, y=0, y=3, about y-axis.
My ans is pie unit^3. Is it correct? if wrong can i know the right calculation.

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asked by ifi
  1. since you are rotating about the y-axis
    our volume will be of the nature
    V = π∫x^2 dy
    = π∫(4/(y+1)^2 dy from y = 0 to 3
    = π∫(4(y+1)^-2 dy from 0 to 3
    = π [ -4(y+1)^-1 ] from 0 to 3
    = π [ -4/(y+1) ] from 0 to 3
    = π ( -4/4 - (-4/1) ]
    = π (-1 + 4 )
    = 3π

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    posted by Reiny

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