6. Consider the two-dimensional plate in the shape of the region bounded by y - 21 and y = 1² with density 6 = x. (a) Sketch a graph of the plate. The graph need not be to scale, but number the axes so that important points can be read from the graph. Shade in the region. 4 (b) Assuming that the mass of the plane is M-3, express y, the y-coordinate of the center of mass of the plane, as a double integral. (e) Find the value of y by evaluating the double integral found in part (b) above.
6. Consider the two-dimensional plate in the shape of the region bounded by y - 21 and y = 1² with density 6 = x. (a) Sketch a graph of the plate. The graph need not be to scale, but number the axes so that important points can be read from the graph. Shade in the region. 4 (b) Assuming that the mass of the plane is M-3, express y, the y-coordinate of the center of mass of the plane, as a double integral. (e) Find the value of y by evaluating the double integral found in part (b) above.
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:6. Consider the two-dimensional plate in the shape of the region bounded by y - 21 and y - 1²
with density 6=z.
(a) Sketch a graph of the plate. The graph need not be to scale, but number the axes so that
important points can be read from the graph. Shade in the region.
4
3'
(b) Assuming that the mass of the plane is M express y, the y-coordinate of the center of
mass of the plane, as a double integral.
(c) Find the value of y by evaluating the double integral found in part (b) above.
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