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Compute the volume of the solid obtained by rotating the region in the first quadrant encolsed by the graphs of the functions y = x^2 and y = sqrt(x) about the y-axis.
I keep getting (1/3)pi and can't figure out what I'm doing wrong!

  • MATH - ,

    rotating about the y -axis needs
    V = π∫x^2 dy

    first equation:
    y = x^2
    2nd equation:
    √x = y
    x = y^2
    x^2 = y^4

    so V = π∫y dy - π∫y^4 dy
    = π [ (1/2)y^2 - (1/5)y^5] from y = 0 to 1
    = π( 1/2 - 1/5)
    = (3/10)π

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