[Steps Shown] The region in the first quadrant bounded by the graphs of y = x and y = x^2 / 2 is rotated around the line y = x. Find the centroid of the region
Question: The region in the first quadrant bounded by the graphs of y = x and y = x^2 / 2 is rotated around the line y = x. Find
- the centroid of the region and
- the volume of the solid of revolution.
Deliverable: Word Document 
(Step-by-Step) Differentiate the function f(x) = xln -x x^5ln x ln
![[Steps Shown] Apply laws of logarithms to](/images/solutions/MC-solution-library-35035.jpg "[Steps Shown] Apply laws of logarithms to simplify the function f(x)=ln")
[Steps Shown] Apply laws of logarithms to simplify the function f(x)=ln
![[See] Find x→ 3lim (2x^4-3x^3-81)/(x^5-10x^3+27) Apply 1’Hopital’s](/images/solutions/MC-solution-library-35036.jpg "[See] Find x→ 3lim (2x^4-3x^3-81)/(x^5-10x^3+27) Apply 1’Hopital’s")
[See] Find x→ 3lim (2x^4-3x^3-81)/(x^5-10x^3+27) Apply 1’Hopital’s
[Solved] Find x→ ∞ lim
Solution: Given f(x) = log10x, find
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