(Solved): Problem 5. Numerical Integration. In water resource engineering, engineers often have to use data ...

Problem 5. Numerical Integration. In water resource engineering, engineers often have to use data from experimental measurements to calculate the stream-cross sectional area \( A_{c} \) \[ A_{c}=\int_{0}^{B} H(y) d y \] where \( B \) is the total channel width, \( H \) is the total depth, and \( y \) is the distance from the bank. Similarly, they also use the experimental data to compute the average flow \( Q \) \[ Q=\int_{0}^{B} U(y) H(y) d y \] where \( U \) is the water velocity. In this problem, you need to approximate \( A_{c} \) and \( Q \) for the following data Compare your answers for the following methods 1. Trapezoidal rule 2. Simpson's (1/3rd) rule