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application of integral

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4. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 2500 pounds per square foot expands to a volume of 3 cubic feet. Find the work done by the gas for the given volume. Assume that the pressure is inversely proportional to the volume.

6. Find moment of mass M_x, M_y, and center of the mass for the laminas of uniform density rho bounded by the graphs of the equations.
x= -y, x=2y, x= 0

Please see the attached file for the fully formatted problems.

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Solution Summary

The solution shows how to use integral to find the work done by a gas (see attachment). It also shows how to calculate the moment of mass and center of mass by integration.

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