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March 29, 2015

March 29, 2015

Posted by **Jack** on Sunday, November 21, 2010 at 8:20pm.

(a) Perpendicular to the x-axis (rectangles)

(b) Perpendicular to the y-axis (triangles)

(c) Perpendicular to the z-axis (rectangles)

- Calculus -
**MathMate**, Sunday, November 21, 2010 at 9:29pmWe do not see the figure, but could probably help anyway.

Along whichever axis you do the integration, the method is to cut up the volume into slices perpendicular to the x-axis, say. Each slice is of thickness dx and the width and height will be a function of y and z, which should in turn be transformed to a function of x. Do the integration along the x-axis and find the volume.

You can proceed in a similar way along the two other axes. The resulting volumes should, of course, be identical.

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