Calculus

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Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2.

A. 8pi/15
B. 32pi/15
C. 64pi/15
D. 4pi/15
E. 16pi/15

  • Calculus -

    v = ∫ πr^2 dx
    where r=2-y
    v = ∫[0,2] π(2-x^2/2)^2 dx

    or

    v = ∫ 2πrh dy
    where r=2-y and h=x
    v = ∫[0,2] 2π(2-y)√(2y) dy

  • Calculus -

    How do you know the r is 2-y and not just y?

  • Calculus -

    Because it is rotated about the line y = 2 ,
    not y = 0 , which would have been the x-axis

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