Numerical Analysis.

Using python, can you show how to solve this problem step by step and provide the code.

Using a) Euler method,b) trapezoid rule, and c) composite Simpsons 1/3 rule.

Let the mesh size be h = 0.05 and compare the numerical solutions with the exact one. Which method give the best estimate and which one give the worst estimate? How many points are required at least to estimate the integral with error 10^10 in each method? Please verify your answer through numerical tests.

Problem 1 (10 pts) Numerically calculate the integral 01xexdx by using Euler method, trapezoid rule, and composite Simpson's 31 rule. Let the mesh size be h=0.05 and compare the numerical solutions with the exact one. Which method give the best estimate and which one give the worst estimate? How many points are required at least to estimate the integral with error 1010 in each method? Please verify your answer through numerical tests. (Hint: for Euler method yi=yi1+hf(ti1,yi1), error y(ti)yi2LhM(eL(tit0)1), where M is an upper bound on the second derivative of y on the given interval and L is the Lipschitz constant of f )