A 5 meter long trough has a crosectional area defined by the function f(x) = -ln(x + 0.01) + e^x and the horizontal line segment given by g(x) = f(0) from x = 0 to the second interception point. Your task is to calculate the volume of the trough. (a) Using MATLAB, plot the cross sectional area of the trough. (b) Using MATLAB's fzero function, find the second intercept of two curves. (c) By hand, calculate the cross sectional area of the trough, and then calculate the volume of the trough. (a) In your own words, explain what numerical integration is (reference any sources you use). (b) Write an m-file that finds the volume of a trough with a cross sectional area defined by a function f(x)and the horizontal line segment given by g(x) = f(0) from x = 0 to the second interception point at x = b. The length of the trough is L meters. The first line of the m-file should be (replace numbers with your student number) function vol = viaduct_volume_n1234567(f, b, L) (c) Use your code to compute the volume of the trough in question 1. compare the two solutions and comment on any differences you observe. (d) What are the limitations to your code