Calculus II

Find the volume of the solid whose base is the semicircle y=sqrt(16−x^2) where −4 is less then or equal to x which is less then or equal to 4, and the cross sections perpendicular to the x-axis are squares.

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  1. Lengths of the sides of these squares are
    equal to y.
    The volume=Int(from -4 to 4)y^2dx=
    2*Int(from 0 to 4)(16-x^2)dx=
    2*(16x-x^3/3)(from 0 to 4)=
    2(64-64/3)

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