[See Solution] Let R be the region bounded by the curves y=x^3, y=2x-x^2 Calculate the area of R Calculate the volume of the solid generated by rotating R

Question: Let R be the region bounded by the curves $y={{x}^{3}}$, $y=2x-{{x}^{2}}$

Calculate the area of $R$
Calculate the volume of the solid generated by rotating R about the x-axis
Calculate the volume of the solid generated by rotating R . about the y-axis
Set up, but DO NOT EVALUATE, an integral for the volume of the solid

generated by rotating R about the line x = 1

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Solution: The downloadable solution consists of 2 pages
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[See Solution] Let R be the region bounded by the curves y=x^3, y=2x-x^2 Calculate the area of R Calculate the volume of the solid generated by rotating R

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