1. Let f(x) = x 2 ln(x). We are interested in the area of the region E enclosed by the lines x = 1 and x = 5, the x-axis, and the graph of f. (a) Use MATLAB (or your preferred plotting software) to graph f on the interval [1, 5]. Include an image of the figure. (b) Make a detailed sketch of the approximating rectangles representing the Riemann sum approximation for the area of E using four subintervals and right endpoints as sample points. Compute the corresponding Riemann sum. (c) Repeat part (b) using eight subintervals instead of four. 2. During the first five seconds of a race, a radar gun is used to record the speed of a runner (in meters per second) at the times (in seconds) given in the following table. Using one- second subintervals and midpoints, estimate the distance covered by the runner in those five seconds. t(s) 0 v (m/s) t(s) v (m/s) 0 3.0 10.51 0.5 4.67 3.5 10.67 1.0 7.34 4.0 10.76 1.5 8.86 4.5 10.81 2.0 9.73 5.0 10.81 2.5 10.22 For the next problem, you will need to use the MATLAB file riemann_sums.m, which can be found in the MATLAB folder within the Files section of Canvas. The function defined. in the m-file takes as input a function f, numbers a and b with a