CALC IINYU Courant Institute of Mathematical SciencesHomework 3, due February 11thCovers 6.5 and 6.6Selin KalayciogluProblem 1(15 points)Most elementary functions do not have elementary antiderivatives. One such function issinxx.(a)(3 points) CalculateZ5π/2π/2sinxxdxusing the trapezoidal rule withn= 4.(b) (3 points) CalculateZ5π/2π/2sinxxdxusing the midpoint rule withn= 4.(c) (3 points) CalculateZ5π/2π/2sinxxdxusing Simpson’s rule withn= 4.(d) (6 points) Given thatd2sinxx<0.25 andd4sinxx<0.13 on the intervalπ5π2, how large shouldnbe to have an error less than 10-4using the midpoint approximation? Using Simpson’s approximation?
Problem 2(28 points)Evaluate the following integrals, and determine whether they converge or diverge. In the instances that you areunable to evaluate the antiderivative, use the comparison test to determine whether the integrals converge ordiverge.