# 1.(a) The function e-x2 does not have an elementary antiderivative, and so numerical integration is the only way to evaluate the integral 01e-x2dx. Using N=4, calculate the values of T and S for this integral, i.e. use the trapezoidal rule and Simpson's rule to approximate the integral.(b) In order to determine how good these approximations are, we need to find upper bounds on the derivatives of f(x)=e-x2. Calculate the derivatives of f and show M2=2 and M4=12.(c) Use the results of part (b) to estimate the errors in the approximations from part (a), which thus gives a pretty good idea of the value of the integral. Finally, determine what value of N would be needed to calculate this integral accurately to six decimal places using Simpson's rule.