Calculus of a Single Variable, Chapter 7, 7.5, Section 7.5, Problem 37

Given pressure is inversely proportional the the volume of the gas,
So, p=k/V
where p is the pressure and V is the volume.
Initial pressure= 1000
Initial volume (V_0) = 2
Final volume (V_1) = 3
Let's calculate k, k=pV
k=(1000)(2)
k=2000
Work done (W) =int_(V_0)^(V_1)k/VdV
=int_2^3(2000)/VdV
Take the constant out,
=2000int_2^3(dV)/V
Use the common integral :intdx/x=ln|x|
=2000[ln|x|]_2^3
=2000[ln(3)-ln(2)]
=2000(1.098612289-0.69314718)
=2000(0.405465108)
=810.9302162
Work done by the gas ~~810.93 foot-pounds.