Calculating work done by a gas

[hraghav]

Homework Statement

An isolated container of a monatomic ideal gas is compressed in such a way that the pressure is linearly proportional to the volume. The pressure can be parametrized as P=αV+Pnot. The gas is initially at atmospheric pressure and room temperature 300K. The initial volume of the container is 0.35m^3. After compression, the gas is allowed to return to room temperature again at a constant volume. What is the temperature inside the container after compression if the final volume is 0.281m^3 and pressure is 357000Pa?
What is the work done by the gas in the container during compression?
What is the pressure of the gas inside the container when the gas has reached room temperature?
What is the change in entropy of the gas as it returns to room temperature?

Relevant Equations

PV = nRT
P = aV + Pnot
W = integral from Vi to Vf of P(V)dv

I have found the answers for T = 848.615K, P = 126137.7705 Pa and change in S = -184.27008 J/K. But my answer for work is not correct and I am not sure where I am making an error. Could someone please help me out with how to calculate work? My steps for work is :

We are given:
Pi = 101325 Pa
Pf = 357000 Pa
Ti = 300 K
Vi = 0.35 m^3
Vf = 0.281 m^3

Using the given equation P = aV + Pnot we can find 'a' which is (357000 - 101325)/(0.281) = 909875.4448 Pa/m^3

For work done we have:

 

[Herman Trivilino]

See the link below for the LaTeX guide. I doubt anyone will want to try to decipher your work in the format you're using.

 

[hraghav]

See the link below for the LaTeX guide. I doubt anyone will want to try to decipher your work in the format you're using.

I did update the question thanks