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.
Christopher R. Johnson
Hamlet Project
Department of Computer Science
University of Utah