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1. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 pounds per square foot expands to a volume of 2 cubic feet. Find the work done by the gas. (Assume that the pressure is inversely proportional to the volume; that is, the gas obeys the ideal gas law such that PV = constant.)

2. Find the indefinite integral and check the result by differentiation:

7. Find

9. Find the partial fraction expansion: (not sure how to handle the exponent of 3 in the denominator.)

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Find the indefinite integral and check the result by differentiation.

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3. A quantity of gas with an initial volume of 1 cubic foot and a pressure of 500 pounds per square foot expands to a volume of 2 cubic feet. Find the work done by the gas. (Assume that the pressure is inversely proportional to the volume; that is, the gas obeys the ideal gas law such that PV = constant.)

Here we will set up the ideal gas law as the equation where k is the constant. We find the value of the constant k using the initial values of P = 500 and V = 1. This gives a value of k = 500 making the function .

We then integrate this function with respect to V over the interval from V = 1 to V = 2. This gives the work done as
.
So, the work done is about 346.6 foot-pounds.

2. Find the indefinite integral ...

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