Work done on a gas as volume decreases

[kabailey]

In a mathematical model, a gas is under a pressure of the form P=e^-v2 (v is volume). Find the work (in Joules) done on the gas as its volume decreases from infinity to zero.



dW = PdV



Solution Attempt:
W=∫₀^∞e^-v2dV

http://en.wikipedia.org/wiki/Gaussian_integral

Gaussian Integral=∫_-∞^∞e^-x2dx=√∏

∴∫₀^∞e^-v2dV

=(√∏)/2|^∞₀

W=(√∏)/2

Is this correct?

 

[kabailey]

anybody?