(a) Evaluate the integral by truncating the interval of integration and using a composite…
(a) Evaluate the integral
by truncating the interval of integration and using a composite quadrature rule. Experiment with both the limits of integration and the step size of the composite rule. Compare your results with the exact value of the integral, which is
(b) Repeat part a, but this time use an adaptive quadrature routine.
(c) Gauss-Hermite quadrature is designed for the interval [−, ] and the weight function exp(−x2 ), so it is ideal for approximating this integral. Look up the nodes and weights for GaussHermite quadrature rules of various orders (see [2, 447, 521], for example) and compute the resulting estimates for the integral.