Question: Suppose that S is a surface which is also a subset of the plane {(x, y, 0): x, y = R}. Let f :

Suppose that S is a surface which is also a subset of the plane {(x, y, 0): x, y = R}. Let f : R R be given by f(x, y, z). Show that the scalar integral fdS is actually just a double integral

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

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 Mathematics Questions!

11 eBook An insurance company must make payments to a customer of $10 million in one year and $4 million in five years. The yield curve is flat at 10%. a. If it wants to fully fund and immunize its...

If you dissolve 8.14 grams of calcium chloride, CaCl 2 , in enough water to make 125.0 mL of solution, what is the molarity of the solution?

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Let f( x, y ) = 7 - x2 + xy- 3y2. (a) Find f (2, 6) and f (2, 6). Fx (2, 6 ) = fy (2, 6) = (b) Interpret the numbers in part (a) as slopes. Of (2, 6) is the slope of the tangent line to the curve of...

I am struggling on answering these questions. I need help on all parts. 1. Given f(x) = Vx + 3 and g(x) = x2. Find (fog) (x) 2. Given f (x) = = and g(x) = x+3. Find (f + g) (2). 3. Given f (x) = x2 +...

Example Math Expression How to Enter the Answer 2 2 uilw -3/5 OO infinity 28 + 1 2^8+1 2+ es 2+exp (5) 5 TL 9 5 * pi / 9 3 In 2 4/7-3*In (2) V2 sqrt (2) 5^ (1/3 ) V5 - e 3 + 2 In(7n) sqrt (5-exp (-3)...

3. Let X be a set and let AX. (i) Define a function A:X{0,1} by the rule A(x)={10ifxAifx/A. The function A is called the characteristic function of A. Show that 1(0)=X\A and that 1(1)=A. When is A a...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

The amount of caffeine (milligrams) in randomly sampled cups of coffee was as follows: a. Find the one-sided 99% confidence interval for the population mean caffeine content of a cup of coffee that...

A steel rod, 10 mm diameter and 50 cm long, is formed into a closed nng and uniformly wound with 400 turns of wire A direct current of 0,5 A is passed through the winding and produces a flux density...

The Foreign Corrupt Practices Act ( FCPA ) of 1 9 7 7 A ) requires auditors to review client's internal control system in a manner which is thorough enough to judge whether client meets the...

Give two examples of countries where capital controls were imposed.

The uniform 30-kg bar OB is secured to the accelerating frame in the 30 position from the horizontal by the hinge at O and roller at A. If the horizontal acceleration of the frame is a = 20 m/s 2 ,...

Consider the following EER diagram that describes the computer systems at a company. Provide your own attributes and key for each entity type. Supply max cardinality constraints justifying your...

The waveform for the current in a 200-yF capacitor is shown in Figure P5.15. Determine the waveform for the capacitor voltage. it)(mA) Figure P5. 15

Consider the voting problem from Exercise C-12.35, but now suppose the integers 1 to k are used to identify k

A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and...

Note that the random variables Q1, . . . ,QN in Section 6.3 have a joint multinomial distribution with probabilities Ï1,Ï2, . . . ,ÏN. Use properties of the multinomial distribution to...

For the data in golfsrs.dat, estimate the proportion of golf courses that have 18 holes, and give a 95% CI for the population proportion.

Investigators in the Wisconsin Department of Natural Resources (1993) used capturerecapture to estimate the number of fishers in the Monico Study Area in Wisconsin. a. In the first study, 7 fishers...

11. Suppose that 3 percent of the people in a population of adults have attempted suicide. It is also known that 20 percent of the population are living below the poverty level. If these two events...

15. Refer to Exercise 14. State in words the event E = (A U B).

16. Refer to Exercise 14. State in words the event F = C).