The Region "R" under the graph of y = x^3 from x=0 to x=2 is rotated about the y-axis to form a solid.(adsbygoogle = window.adsbygoogle || []).push({});

a. Find the area of R.

b. Find the volume of the solid using vertical slices.

c. Find the first moment of area of R with respect to the y-axis. What do you notice about the integral?

d. Find the x coordinate of the centroid of R.

e. A theorem of Pappus states that the volume of a solid of revolution equals the area of the region being rotated times the distance the centroid of the region travels. Show that this problem confirms this theorem.

3. The attempt at a solution

I was able to do part "a" as the integral from 0 to 2 of x^3 dx. Also I believe part "b" is pi*[3y^(5/3)/5] evaluated from 0 to 2

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# Homework Help: Work, Pappus Theorem

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