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Prove that if the figure S is bounded by a simple convex contour and is situated between the ordinates y_(1) and y_(2), then the volume of the solid generated by revolving this figure about the x-axis can be expressed by the formula V= 2pi int_(y_(1))^(y_(2)) yh dy, where h= x_(2) (y) - x_(1) (y), x= x_(1) (y) being the equation of the left portion of the contour and x= x_(2) (y) that of the right portion. |
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