Question: Let S be the surface of the box enclosed by the planes x = 1, y = 1, z = 1. Approximate S cos(x

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

Step by Step Solution

★★★★★

3.26 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The box is a cube where each face has surface area 4 The cen... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

The Bender Construction Co. is involved in constructing municipal buildings and other structures that are used primarily by city and state municipalities. This requires developing legal documents,...

Use the Divergence Theorem to calculate the surface integral S F dS; that is, calculate the flux of F across S. F(x, y, z) = x 2 yz i + xy 2 z j + xyz 2 k, S is the surface of the box enclosed by...

Let x1 .... xr be eigenvectors of an n x n matrix A and let S be the ssubspace of R spanned by x1. x2 ....xf Show that S is invariant under A (i.e.. show that Ax S whenever x 5).

Let S be the standard basis for Rn. Prove Theorem 8.6.2 by showing that the linear transformation T: V Rn that maps v V to its coordinate vector (v)s in Rn is an isomorphism.

Use the Divergence Theorem to calculate the surface integral S F ds; that is, calculate the flux of F across S. F(x, y, z) = e x sin yi + e x cos yj + yz 2 k, S is the surface of the box bounded by...

QUESTION 1: Find the flux of the vector field 1?\" = (y, z, 3:) across the part of the plane .2 = 2 + 433 + 3y above the rectangle [0, 2] x [0, 3] with upwards orientation. Question Help: Video...

I need help, look the image, show step and solution 1) Let be F(x, y, z) = (2xy2 + z, 2x y + 2y, x) and C the parameterization curve r(t) = (sen8 ( t) + 1,(3,18) with te [0, 1]. Find F. dr C...

Problems 11, 13, 18, 22, 33 please 94 CHAPTER 1 . FUNCTIONS OF SEVERAL VARIABLES SECTION 1.8 EXERCISES Review Questions 1. Describe the appearance of a smooth surface with a local maxi- 30. f(x, y) =...

1 State whether the given equation is an ellipsoid, a hyperboloid, an elliptic cone or a paraboloid. If it is a hyperboloid, state whether it is of one sheet or two sheets. x 2 + 2y 2 + 3z 2 = 1 2....

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

All securities purchases made by Mechanical Engineers, Inc. described in this problem represent less than a 20% interest in the investee companies. Part I: Mechanical Engineers, Inc. made the...

Is it true sulfuric acid reacts with many metals? Options 1) True 2) False

A company that sells multiple types of products has a combined selling price per unit $ 1 5 0 combine variable cost per unit of $ 5 0 in total fixed cost of $ 2 5 , 0 0 0 the way to average...

11-10 Research ways in which marketers protect against the consequences of online pricing errors and write a brief report summarising what you learn. (AACSB: Communication; Reflective thinking) pg94

What is the change in population 4 during these years? The following table describes populations that are growing through immigration or emigration. For each, sketch a graph, find the number of...

On island 1. Suppose the states of populations on four islands are described in the following table. For each, illustrate what is happening with a graph, and describe it in words. Does any of the...

On island 2. Suppose the states of populations on four islands are described in the following table. For each, illustrate what is happening with a graph, and describe it in words. Does any of the...

2) SoftTech Inc is a small manufacturer of entertainment software that reporte revenues of $ 25 million in the most recent financial year. You expect the firm to grow significantly over time and...

LPT inc. is an integrated oil company headquartered in Dallas, Texas. The company has three operating divisions: oil exploration and production (commonly referred to as E&P), pipelines, and refining....

Meadow Company wants to invest its net profits of $123,000 for 3 years in either a credit union or a local bank. The credit union provides interest of 3.25% compounded monthly, while the local bank...