A researcher is investigating the velocity of air flowing through a pipe at different pipe radii from the centreline of a circular pipe to compute the mass flow rate of air in the pipe. Velocity data for air collected at different radii of a 0.08-m diameter pipe is as tabulated in Table 2. Table 2: Air velocity data at different pipe radius Radius, r (m) Velocity, v (m/s) 0 0.01 0.02 0.03 0.04 10.0 8.3 6.2 3.6 0 It is known that the mass flow rate, M (in kg/s) can be computed using the following equation: 0.04 M = pv2лr dr where p is 1.2 kg/m³, v is the air velocity in m/s, x is 3.1416 and r is the pipe radius in m. (a) Estimate the mass flow rate, M (in kg/s) of air in the pipe using: (i) suitable Trapezoidal rule (ii) suitable Simpson's rule (b) Given the true value of 0.0252 kg/s, calculate the true percent relative errors, using your solutions from part a(i) and a(ii). Comment on the accuracy of your findings.