With a programmable calculator or a computer it is possible

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 end points for n = 10, 30, 50, and 100. (Round your answers to four decimal places.)

The region under

y = 5 cos x

from 0 to pi/2

Solution

For n = 10 use

=SUMPRODUCT(PI()/2/10*5*COS(PI()/2* ROW(1:10)/10))

For n = 30, change all the 10\'s in the formula to 30.