5. Find the moments Mx and My of the lamina above the rectangle with vertices (0,0), (0,2), (3,2), and (3,0) with density function p(x) = 3x² + xy².
5. Find the moments Mx and My of the lamina above the rectangle with vertices (0,0), (0,2), (3,2), and (3,0) with density function p(x) = 3x² + xy².
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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Would someone be able to check my work for number 5? Thanks!
![5. Find the moments Mx and My of the lamina above the rectangle with vertices
(0,0), (0,2), (3,2), and (3,0) with density function p(x) = 3x² + xy².
3 2
3
3x°y + x-4 g°] dx = } 3()+ x(2} -(0) dx
to
%3D
) bx
bx
54 + 12 = b6
32
2
3
3
=Sb x² + 4X dx =
**41 + (-0 = 54 +18 (2 = Mx
3 2
My=
O D
4,
bz + * dz = )* (5o)= 121-5 + 24 145.5 = My
8(3)
6. Find the center of mass of the lamina with density function p(x) = 2y + 6x in
the region R = {(x, y)|0 < x < 2,0 < Y< 3}.
3
m =
9+ 18x dx
j 18+ 27xdx = 1sx+ 27* = 18(6) + 22 (2) = 36 +54 = 190
%3D
O 2 3
23
+ bx uT dx =
1823
= 18 + 48 =l
= bb = l
= 90
54
54](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8854ffd-431b-44a2-b47e-daec534c3a26%2F8f5956e6-f9bb-4e30-bdcb-7e5c6e79ba8f%2Fs7r8x9a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Find the moments Mx and My of the lamina above the rectangle with vertices
(0,0), (0,2), (3,2), and (3,0) with density function p(x) = 3x² + xy².
3 2
3
3x°y + x-4 g°] dx = } 3()+ x(2} -(0) dx
to
%3D
) bx
bx
54 + 12 = b6
32
2
3
3
=Sb x² + 4X dx =
**41 + (-0 = 54 +18 (2 = Mx
3 2
My=
O D
4,
bz + * dz = )* (5o)= 121-5 + 24 145.5 = My
8(3)
6. Find the center of mass of the lamina with density function p(x) = 2y + 6x in
the region R = {(x, y)|0 < x < 2,0 < Y< 3}.
3
m =
9+ 18x dx
j 18+ 27xdx = 1sx+ 27* = 18(6) + 22 (2) = 36 +54 = 190
%3D
O 2 3
23
+ bx uT dx =
1823
= 18 + 48 =l
= bb = l
= 90
54
54
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