Question

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 = 3 cos(x) from 0 to π/2

n	Sum of Areas
10	?
30	?
50	2.9526
100	?

Guess the value of the exact area. ?

Answer 1

Given in

Right end point uses the right endpoint of the sub-interval

Area of approximating rectangle is given by

for n=10,

Dividing interval into subintervals

for n=30,

dividing interval into sub intervals

for n=100,

dividing interval into sub intervals