Assignment:
Q1. 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.)
Q2. Find the indefinite integral and check the result by differentiation: ∫u2√u3 + 2 du
Q3. Find ∫ dx/ x2√9 - x2
Q4. Find the partial fraction expansion: 4x2 + 3 /(x - 5)3 (not sure how to handle the exponent of 3 in the denominator.)
Provide complete and step by step solution for the question and show calculations and use formulas.