Chapter 5.1, Problem 28E

With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of $n$ , using looping. (On a TI use the Is > command or a For-EndFor loop, on a Casio use Isz, on an HP or in BASIC use a FOR-NEXT loop.) Compute the sum of the areas of approximating rectangles using equal subintervals and right endpoints for $n=10,30,50$ , and 100 . Then guess the value of the exact area.

28. The region under $y=\cos x$ from 0 to $\pi /2$