Prove the following two theorems of Pappus: The area A inside a closed curve in the x , y plane, y ≥ 0 , is revolved about the x axis. The volume of the solid generated is equal to A times the circumference of the circle traced by the centroid of A. Hint: Write the integrals for the volume and for the centroid.
Prove the following two theorems of Pappus: The area A inside a closed curve in the x , y plane, y ≥ 0 , is revolved about the x axis. The volume of the solid generated is equal to A times the circumference of the circle traced by the centroid of A. Hint: Write the integrals for the volume and for the centroid.
The area A inside a closed curve in the
x
,
y
plane,
y
≥
0
, is revolved about the
x
axis. The volume of the solid generated is equal to A times the circumference of the circle traced by the centroid of A. Hint: Write the integrals for the volume and for the centroid.
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