1. Use Romberg integration to evaluate the integral 021+x2exsinxdx to an accuracy of 0.5% or less. In other words, pick an interval x and use it with the trapezoidal rule. Then cut the interval in half, use the trapezoidal rule again, and use Romberg integration to estimate a better value for the integral. Cut it in half again, use the methods of Romberg integration, and then use those methods again with the two estimates. Continue until the integral changes by less than 0.5%. Reminder: the equation for the first Romberg integration is IA=34I231I1. The equation for the second Romberg integration (using two IA results for increasing numbers of intervals) is Ia=1516IB151IA. See lecture 20.5 for a Romberg integration example