4. A thin lamina with constant density 5 g/cm² covers the region R bounded by y = ff(x) = 20x - x² and the x-axis. (a) Find the total mass of the lamina. First write down a definite integral for the value, and then use a calculator to find the exact value of the mass. (b) Find the coordinates (,) of the center of mass of the lamina. First write down a definite integral for each related value, and then use a calculator to evaluate, giving an answer rounded off to two decimal places for each coordinate. (c) Sketch the center of mass (.) on the graph.
4. A thin lamina with constant density 5 g/cm² covers the region R bounded by y = ff(x) = 20x - x² and the x-axis. (a) Find the total mass of the lamina. First write down a definite integral for the value, and then use a calculator to find the exact value of the mass. (b) Find the coordinates (,) of the center of mass of the lamina. First write down a definite integral for each related value, and then use a calculator to evaluate, giving an answer rounded off to two decimal places for each coordinate. (c) Sketch the center of mass (.) on the graph.
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:4. A thin lamina with constant density 5 g/cm² covers the region R bounded by
y = ff(x) = 20x - x² and the x-axis.
(a) Find the total mass of the lamina. First write down a definite integral for the value, and then use a
calculator to find the exact value of the mass.
(b) Find the coordinates (,) of the center of mass of the lamina. First write down a definite integral
for each related value, and then use a calculator to evaluate, giving an answer rounded off to two decimal
places for each coordinate.
(c) Sketch the center of mass (,) on the graph.
100
80
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