Fall 2017 MTH 1120 You must show all work to receive full credit. Be neat and organized, and use correct notation. Extra Credit All work is to be your own. Eric Pauley Plagiarizing is prohibited. 15:00 IS: 1S 1. Numerical Integration Consider the definite integral dz Jo V1+2 is done and shade the region that represents "area under the curve (b) Evaluate the definite integral above exactly using calculus techniques. (a) Sketch the graph of the integrand, indicating the closed interval over which the integration 2 points 2 points (c) Use Excel to approximate numerically tue varue of the above definite integral, that is caleu- late the discrete sum in where Ar = ì¤ , and is chosen to be the midd point of the subinterval Ixk,Tk+11. Using 4 points 4 points 2 points i, n=10 ii, n= 40 (d) Compare and comment-on your results in parts (b) and (c). Newton's Method (a) State the "estimate update" rule used in Newton's Method to approximate a solution to 2 noinmts