Verify Stokess Theorem by evaluating as a line integral and as a double integral. F(x, y, z)

Question:

Verify Stokes’s Theorem by evaluating

as a line integral and as a double integral.

F(x, y, z) = (cos y + y cos x)i + (sin x - x sin y)j + xyzk

S: portion of z = y2 over the square in the xy-plane with vertices (0, 0), (a, 0), (a, a), and (0, a)

N is the upward unit normal vector to the surface.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781285057095

10th Edition

Authors: Ron Larson, Bruce H. Edwards

See More Books

Question Posted: Apr 05, 2023 01:02 AM

See More Questions

A surface S2 consists of that part of the cylindrical surface z+y? = 9 that lies between the planes z=0 and z=2, and for which z> 0, as shown in Figure Q2. (a) Figure Q2.a on page 4 shows an attempt...
In Problems 1-3, use Stokes's Theorem to calculate? 1. F = x2 i + y2 j z2 k; S is the hemisphere z = (1 - x2 - y2 and n is the upper normal. 2. F = xy i + yz j + xy k; S is the triangular surface...
In Problems 1-3, use Stokes's Theorem to calculate? 1. F = 2zi + x j + 3y k; C is the ellipse that is the intersection of the plane z = x and the cylinder x2 + y2 = 4, oriented clock wise as viewed...
What is the square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power?
Plum Corporation will begin operations on January 1. Earnings for the next five years are projected to be relatively stable at about $80,000 per year. The shareholders of Plum are in the 33% tax...
Jose Loder established Bronco Consulting on August 1, 2014. The effect of each transaction and the balances after each transaction for August are shown below. Instructions 1. Prepare an income...
For each of the following situations, calculate a $95 \%$ confidence interval for the mean ( $\sigma$ known), beginning with the step, "Identify the critical value of $z$." X = 7.00, o Xe =...
Sunlight is used in a double-slit interference experiment. The fourth-order maximum for a wavelength of 450 nm occurs at an angle of = 90o. Thus, it is on the verge of being eliminated from the...
Prepare the schedule of cost of goods manufactured for Barton Company using the following information for the year ended December 31. Direct materials used Direct labor Factory overhead Work in...
Find the divergence of the vector field F. F(x, y) = xe x i + ye y j
Find the divergence of the vector field F. F(x, y) = xi + 2yj
A human heart beats 72 times every minute. How many times, on average, does a heart beat during a healthy 70 -year lifespan?
In a two phase $A C$ servo motor with small $X / R$ ratio, maximum torque occurs at (a) synchronous speed (b) low speed (c) high speed (d) rated speed.
Match the control system components in List I with their function in List II and select the correct answer using the codes given below the lists: List I A. Servo motor B. Amplidyne C. Potentiometer...
Which of the following can be included in a control system such that total number of poles and zeros, does not change? (a) Amplidyne (b) DC servo motor (c) tachometer (d) AC servo motor.
The linear model of a robot arm system being driven by a DC motor, is shown in Fig. P 9.9 (a). The system variables and parameters are given below: (a) Write equations describing dynamics of system...
In case of synchro error detector, the electrical zero position of control transformer is obtained when angular displacement between rotors, is (a) $0^{\circ}$ (b) $45^{\circ}$ (c) $90^{\circ}$...
Andrea loves to eat burritos with hot sauce. In fact, she cannot enjoy a burrito (B) unless it has three servings of hot sauce (H). She gets no additional enjoyment from more than three servings per...
A consumer magazine is evaluating five brands of trash compactors for their effectiveness in reducing the volume of typical household products that are discarded. In the experiment, each block...
Use the methods introduced in Section 7.1 to evaluate the following integrals. ^x + 3x + 1 dx x' + 1
Use the methods introduced in Section 7.1 to evaluate the following integrals. Let u = t - 1. Vi - I 1 dt 2t
Use integration by parts to evaluate the following integrals. cln 2 3t dt et -1
On its June 30, 2015 balance sheet, Barrows Corporation has total assets of $100,000, current liabilities of $40,000, and owners' equity of $60,000. Which one of the following statements must be true...
You observe that in a given data set, when P of an ice-cream rises from $1 to $2, Q demanded rises from 400 units to 500 units. Can Anya thus declare that Law of Demand does not always work, or could...
6.What is the implication for the Management Reporting System of an organization that implements the formalization of tasks principle? 7.What are the reasons the companies use coding schemes in their...

Verify Stokess Theorem by evaluating as a line integral and as a double integral. F(x, y, z)

Question:

JC F. dr

Step by Step Answer:

Fx y z cos y y cos xi sin x x sin yj xyzk S portion of z y over the sq...View the full answer

Calculus

Students also viewed these Mathematics questions