Integral Calculus and Simspon rule

I recently post/ed this question but did not finish it. Would you please tell me what I have to do next,

Question:

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, (Hydropneumatic Accumulators - HydroTrole Limited) is being factory tested for certification purposes.

The following data has been collected by a technician:

- Gas volume:
*V *= 0.8 m^{3} - Gas pressure:
*p *= 160 kPa - Compression index:
*n *= 1.4 - Pressure/volume relationship:
*pV*^{n} = *C * - Work done = Integral sign top( V2) bottom= V1 pdV

You first need to work out *C, *the value of the pressure/volume relationship.

Calculate the work done in compressing the nitrogen from 0.8 m^{3} to 0.6 m^{3} using:

- integral calculus
- Simpson’s rule

Comment on the accuracy of the numerical method.

**Note**: if you wish, you may use a spreadsheet for the numerical method.

Update

Edited out the answer:

THANKS

Re: Integral Calculus and Simspon rule

I looked at your spread sheet and it looks like you are integrating the pressure. The problem asks you to integrate "V dP".

Also, please remove the link to a commercial site or this thread will be deleted.

Re: Integral Calculus and Simspon rule

That is correct sir. I have already completed this work before but forget it. How would I be able to calculate the integral calculus. I know the answer is 39026.4552