The curves y = 2x - x 2 and y = 3x2 - 6x are used to form the boundary of a thin plate of uniform density. Make sure you simplify and put in lowest terms. a. Set up and evaluate the integral for finding the total mass (m). b. Set up and evaluate the integral for finding the moments about the x-axis (Mx). C. Set up and evaluate the integral for finding the moments about the y-axis (My).

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Chapter65: Achievement Review—section Six
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The curves y = 2x - x 2 and y = 3x2 - 6x are used to form the boundary of a thin plate of
uniform density. Make sure you simplify and put in lowest terms.
a. Set up and evaluate the integral for finding the total mass (m).
b. Set up and evaluate the integral for finding the moments about the x-axis (Mx).
C. Set up and evaluate the integral for finding the moments about the y-axis (My).
d. Find (x, y).
e. Use the Theorem of Pappus to find the volume of the solid of revolution by rotating the thin
plate about the y-axis.
Transcribed Image Text:The curves y = 2x - x 2 and y = 3x2 - 6x are used to form the boundary of a thin plate of uniform density. Make sure you simplify and put in lowest terms. a. Set up and evaluate the integral for finding the total mass (m). b. Set up and evaluate the integral for finding the moments about the x-axis (Mx). C. Set up and evaluate the integral for finding the moments about the y-axis (My). d. Find (x, y). e. Use the Theorem of Pappus to find the volume of the solid of revolution by rotating the thin plate about the y-axis.
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