   Chapter 16.7, Problem 1E

Chapter
Section
Textbook Problem

Let S be the surface of the box enclosed by the planes x = ±1, y = ±1, z = ±1. Approximate ∬S cos(x + 2y + 3z) dS by using a Riemann sum as in Definition 1, taking the patches Sij to be the squares that are the faces of the box S and the points to be the centers of the squares.

To determine

To find: The approximate value of Scos(x+2y+3z)dS .

Explanation

Given data:

x=±1,y=±1 and z=±1 , that is the centers of the faces are (±1,0,0),(0,±1,0) and (0,0,±1) .

The box is a cube and the surface area has 4.

Find Scos(x+2y+3z)dS .

Scos(x+2y+3z)dS{[cos(1+2(0)+3(0))](4)+[cos(1+2(0)+3(0))](4)+[cos(0+2(1)+3(0))](4)+[cos(0+2(1)+3(0))](4)+[cos(0+2(0)+3(1))](4)+[cos(0+2(0)+3(1))](<

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