Question: Evaluate the surface integral. S F dS, where F(x, y, z) = xz i - 2y j + 3x k and S is

Evaluate the surface integral.

∫∫S F • dS, where F(x, y, z) = xz i - 2y j + 3x k and S is the sphere x2 + y2 + z2 = 4 with outward orientation

Step by Step Solution

★★★★★

3.42 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since the sphere bounds a simple solid region the Divergence Theorem applies and SSF ds SSS di... View full answer

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 Precalculus Questions!

Q:

Evaluate the surface integral. S (x 2 z + y 2 z) dS, where S is the part of the plane z = 4 + x + y that lies inside the cylinder x 2 + y 2 = 4

Q:

Use the Divergence Theorem to calculate the surface integral s F dS, where F(x, y, z) = x 3 i + y 3 j + z 3 k and S is the surface of the solid bounded by the cylinder x 2 + y 2 = 1 and the planes z...

Q:

Solve the differential equation. y'' - y' - 6y = 0

Q:

Can someone solve this? (1 point) Evaluate the surface integral S F . dS where F = (-x, 5z, -5y) and S is the part of the sphere x2 + y2 + 22 =9 in the first octant, with orientation toward the...

Q:

14. [14] Use the Divergence Theorem to evaluate the surface integral ff F . dS for F (x, y, z) = where S is the surface of the solid bounded by the paraboloid z = 9 -x2 - y and the xy-plane, with...

Q:

solve it with proper solution VA Topic 9 - HW 3: (Surface Integrals X VA Topic 9 - HW 4: (Stokes' Theorem X + X > C A webassign.net/web/Student/Assignment-Responses/last?dep=24613344 . .. 9. [-/1...

Q:

the answer is Please provide a detailed explanation of the answer 4. Consider the vector field F = (, y, 23). (a) By expressing all quantities in terms of spherical polar coordinates, find an expres-...

Q:

Evaluate the surface integral S F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward)...

Q:

Evaluate the surface integral S F dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward)...

Q:

6. Evaluate the surface integral JJ F dS for the vector field F(x, y, z) = yi + xj, where S is the surface given by x2 + y2 + z2 = 4 in the first octant (x 2 0, y 2 0, z 2 0). Note: Flux Integrals:...

Q:

Code is a symbolic representation of __________information. a) Continuous b) Discrete c) Analog d) Both continuous and discrete

Q:

How much diluent is needed to fill a size 1 capsule that also contains 55 mg of the drug? If size 1 capsules are individually filled with the components, 500 mg of the drug and 330 mg of the diluent...

Q:

1. LO.1, 6 Eggshell, Inc., a C corporation, operates a rental clothing store, and its profits are subject to double taxation. First Church of the States operates a retail gift shop and bookshop and...

Q:

Do economic growth and sound environmental policy necessarily conflict? Identify some areas where a choice must be made between economic growth and environmental preservation and others where the two...

Q:

Find the expected number remaining inside as a function of time. 40 molecules begin inside a cell. Each leaves independently with probability 0.2/min.

Q:

Two or fewer out of eight offspring are tall. Suppose that the allele A for height is dominant, meaning that plants with genotypes AA and Aa are tall, while those with genotype aa are short. If an Aa...

Q:

Example 6.1.5 from Section 6.1, which illustrates stochastic immigration, was generated by adding two individuals with probability 0.5 and zero individuals with probability 0.5 for 100 generations....

Q:

An IBM bond pays 7% interest, and a Florida State bonds pays 5%. If you are in a 40% tax bracket, which should you purchase? ( Assume that the level of risk is the same for both bonds.)

Q:

You own a portfolio consisting of the following stocks: Percentage of Portfolio, Beta, Expected Return 1. 5% 1.20 14%, 2. 25 0.65, 10, 3. 15 1.00 12, 4. 20 1.4 16, 5. 35 0.90 11. The risk-free rate...

Q:

1. A law firm plans to invest in a small business computer system. The initial investment is $35,000. The firms tax rate is 40%. The computer system should provide additional revenue of $25,000 per...