A lamina with density function given by p(x, y) = sin(x² + y²) is defined on the half- disk x = /1- y?, x 2 0. a. Set up a double integral to compute the mass of the region. Evaluate the integral. b. Set up a double integral to find the x-coordinate of the center of mass. Use a calculator to estimate it to two decimal places. c. Set up a double integral to compute the y-coordinate of the center of mass. Explain why this integral will yield a value of zero. Then state the center of mass.

A lamina with density function given by p(x, y) = sin(x² + y²) is defined on the half- disk x = /1- y?, x 2 0. a. Set up a double integral to compute the mass of the region. Evaluate the integral. b. Set up a double integral to find the x-coordinate of the center of mass. Use a calculator to estimate it to two decimal places. c. Set up a double integral to compute the y-coordinate of the center of mass. Explain why this integral will yield a value of zero. Then state the center of mass.

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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Question

7. A lamina with density function given by p(x, y) = sin(x² + y²) is defined on the half-
disk x = /1- y², x 2 0.
a. Set up a double integral to compute the mass of the region. Evaluate the
integral.
b. Set up a double integral to find the x-coordinate of the center of mass. Use a
calculator to estimate it to two decimal places.
c. Set up a double integral to compute the y-coordinate of the center of mass.
Explain why this integral will yield a value of zero. Then state the center of mass.

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