Problem 2(40pts): We can calculate the volume of a system as V=abP(x)dx.P(x) function values against x values were obtained experimentally as follows: a) Calculate the system volume (V) using Simpson's 1/3 rule ( 2 segments application). (20 pts) (Correct solution set up is 10pts and correct result is 10pts ) b) If f(x)=(V1.85792e3110)2.05, find the root of the function using the Newton-Raphson Method. ( 6 significant digits solution, 5=103 and x0=0.5 ) Note: V is calculated in part a. (20 pts) (Correct solution set up is 10pts and correct results are 10pts)