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Yes, we do not actually integrate in any problems. It is used to derive the 2 formulas (constant pressure vs variable). Lavelle uses it to explain why we use natural logarithms in the w = nRT ln (v1/v2) equation
In a way it could be considered to be a form of obtaining w=-P times delta V; however, this equation is used to during an irreversible pathway which is temperature (T) changes along a pathway decrease then increase work done against constant Pex. The integral form of obtaining work done in a system is referred to as a reversible pathway because constant temperature along a pathway the volume increase while the pressure decreases having more work done. In addition, the integral is used in a reversible pathway because there is a change in volume when the work is being done.
In this class, yes the integral is only used to find the -PdV equation that we use. The integral is solved in order to show that pressure is constant and that volume is changing in small steps so we can just say that dV=V2-V1.
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