- #1

Pirata

- 2

- 0

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.

## 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