Clear handwriting

Clear handwriting

Question 1: A function and its integral form are given by following cquations. f(x)=1xI=abf(x)dx=13f(x)dx (a) Draw an approximate graph (Take x:1 io 3) to identify if this function represcuts a linear or nonlinear behavior and use basie calculus concepts (Analytical Method) to calculate its exact inteseal. (b) Formulate a numerical integration formula cmploying three point Gauss-Legendre method to calculate its approximate integral and absolute true emor (c) Solve to determine approximate integral employing Simpson's 1/3 Rule and absolute true error (d) Compare absolute error answers from (b) and (c) and identify which method is superior. (e) Formualte an appropriate 2-point forward or backward or central difference formula to find first derivative at x=1 (take step size =1 ). Also calculate absolute true error