Consider the integral: .
1. Use Simpson’s rule and Gaussian quadrature (with 2, 3, or 4 nodes) to calculate the integral using4,8,16, and 32 intervals. Plot the error versus the number of points in a log-log plot.
2. Develop a quadrature method based on cubic spline interpolation.
3. Use the cubic spline-quadrature method developed in part 2 to calculate the integral. Discuss the errorfor numerical integrations by varying the number of intervals.
4. Use the Monte-Carlo method to calculate the integral.
