Visualizing the Trapezoidal Method

Just as we used Maple to visualize the rectangular method, we can use it to visualize the trapezoidal method:

animtrap(x->x^2, 0, 1, 6);

This animation is similar to the one that we showed you for the rectangular method. We are using the same function, the same endpoints, and the same number of frames. The only difference is that we are approximating the area with trapezoids instead of with rectangles. As before, the number of trapezoids doubles with each successive frame. You will find it instructive to compare the trapezoidal animation with the rectangular animation. This will give you a clear impression of how much faster the trapezoidal method converges.