Pappuss Theorem Let A be the area of the region D between two graphs y = g1(x) and y =
Chapter 15, Problem 60(choose chapter or problem)
Pappuss Theorem Let A be the area of the region D between two graphs y = g1(x) and y = g2(x) over the interval [a, b], where g2(x) g1(x) 0. Prove Pappuss Theorem: The volume of the solid obtained by revolving D about the x-axis is V = 2Ay, where y is the y-coordinate of the centroid of D (the average of the y-coordinate). Hint: Show that Ay = b x=a g2(x) y=g1(x) y dy dx 61
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