   Chapter 4.1, Problem 10E

Chapter
Section
Textbook Problem

# 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.The region under y = cos x from 0 to π / 2

To determine

To compute:

The sum of the area of approximating rectangles using equal subintervals and right endpoints

Explanation

1) Concept:

Use a programmable calculator to find the Riemann sum.

2) Given:

The region is under y=cosx from  0  to  π/2

3) Calculation:

The algorithm for calculating the Riemann sum includes the following steps.

1) Let SUM = 0, X_MIN = 0, X_MAX =pi/2, N = 10

DELTA_X = (X_MAX X_MIN/N), RIGHT_ENDPOINT = X_MIN +DELTA_X

2) Repeat steps 2a and 2b in sequence until RIGHT_ENDPOINT > X_MAX

At the end of this procedure, (DELTA__X)* SUM   is the answer

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