Calculus

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Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis.

  • Calculus -

    the intersect at (0,0) and (2,4)

    since we are rotating around the y axis we need the radius squared, that is, we need the x^2 of each equation
    from the 1st : y = 2x --> x = y/2 , then x^2 = y^2/4
    from the 2nd: y = x^2 ---> then x^2 = y , the outer
    so volume
    = π∫(y - y^2/4) dy from y = 0 to 4
    = π[y^2/2 - y^3/12] from 0 to 4
    = π(16/2 - 64/12 - 0)
    = 8π/3

    check my arithmetic

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