6. A fluid is flowing through a pipe, which has circular cross-section. The following table gives the approximate speed and density at different radii: r (cm) v (m/s) (kg/m3) 0 1.6 3.2 4.8 6.4 7.47 7.87 7.95 8 10 9.69 9.3 8.77 7.95 6.79 5.57 4.89 0 0.9 0.947 0.950 0.958 1.025 1.127 1.185 1.192 1.2 The mass flow rate is found by integrating R dm =m= vdA= v 2 rdr dt 0 where R = the maximum radius of the pipe. (a) Find the mass flow rate using the trapezoidal rule. (b) Find the mass .ow rate by first interpolating the data using a cubic spline to obtain 20 equally spaced intervals. Then use both trapezoidal rule and Simpson's rule to find the mass .ow rate. (c) Discuss your results