calculus

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the region bounded by the quarter circle (x^2) + (y^2) =1. Find the volume of the following solid.

The solid whose base is the region and whose cross-sections perpendicular to the x-axis are squares.

  • calculus -

    "The solid whose base is the region and whose cross-sections perpendicular to the x-axis are squares."
    means that z=2y
    but since y=2sqrt(1-x^2) (on the circle), so z=2sqrt(1-x^2)

    For example, at x=0, z=1,
    at x=1, z=0.


    The volume of the solid is then
    ∫∫∫dx dy dz
    where the limits of integration are
    for z: 0 to 2sqrt(1-x^2)
    for y: -sqrt(1-x^2) to sqrt(1-x^2)
    for x: -1 to 1

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