3. A thin plate (or "lamina") occupies the region bounded by the graphs of y = x² and x = 4y². This plate has a constant density of p = 20m Sketch this region, and then find both the mass of the plate, and the center of mass of the plate. You should set up an integral for each value, explaining how you set it up, and then integrate by hand, showing each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a calculator). For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places.
3. A thin plate (or "lamina") occupies the region bounded by the graphs of y = x² and x = 4y². This plate has a constant density of p = 20m Sketch this region, and then find both the mass of the plate, and the center of mass of the plate. You should set up an integral for each value, explaining how you set it up, and then integrate by hand, showing each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a calculator). For each quantity, give both the exact value and a decimal approximation that is accurate to three decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3.
A thin plate (or "lamina") occupies the region bounded by the graphs of
gm
y = x² and x = 4y². This plate has a constant density of p = 20 cm²
Sketch this region, and then find both the mass of the plate, and the center of mass of the plate. You
should set up an integral for each value, explaining how you set it up, and then integrate by hand, showing
each step, and evaluating at the limits using the Fundamental Theorem of Calculus (rather than just using a
calculator). For each quantity, give both the exact value and a decimal approximation that is accurate to
three decimal places.
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