Calculus

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Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6

  • Calculus -

    y=2 intersects xy=6 at (3,2)
    So we are rotating the region bounded by
    (3,2) to (6,2), then down to (6,1) and joining the curve back to (3,2)

    Vol = π∫(6-x)^2 dy from y = 1 to 2
    = π∫(36 - 12x + x^2) dy
    =π∫(36 - 12(6/y) + 36/y^2) dy from 1 to 2
    = π[ 36y - 72lny - 36/y ] from 1 to 2
    = π( (72 - 72ln2 - 18) - (36 - 72ln1 - 36) )
    = π(54 - 72ln2)
    = 18π(3 - 4ln2) or appr 12.86

    check my arithmetic

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