Some computer algebra systems have commands that will draw approximating rectangles and evaluate the sums of their areas, at least if xi is a left or right endpoint. (For instance, in Maple use left box, right box, left sum, and right sum.)
(a) If f(x) = √x, 1 < x < 4 find the left and right sums for n = 10, 30, and 50.
(b) Illustrate by graphing the rectangles in part (a).
(c) Show that the exact area under f lies between 4.6 and 4.7.