Posted by mike on Sunday, October 28, 2012 at 6:42pm.
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 crosssections perpendicular to the xaxis are squares.

calculus  MathMate, Sunday, October 28, 2012 at 7:12pm
"The solid whose base is the region and whose crosssections perpendicular to the xaxis are squares."
means that z=2y
but since y=2sqrt(1x^2) (on the circle), so z=2sqrt(1x^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(1x^2)
for y: sqrt(1x^2) to sqrt(1x^2)
for x: 1 to 1
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