Question

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) = 3xy2 i + xez j + z3 k
S is the surface of the solid bounded by the cylinder y2 + z2 = 9 and the planes x = -1 and x = 3.

Expert Answer

1 Rating

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Applications of Integration

Integration

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: Find an equation of the tangent plane to the graph of f (x, y) = xy 2 - xy + 3x 3y at P = (l, 3).

A: Click to see the answer

Q: Please find the area of the specified region. Thank you!

A: Click to see the answer

Q: Find the area of the shaded region in the following figure y = sin x 5п

A: Find the functions f (x) and g (x).

Q: Can someone show me how to do this? mostly the limits on part a, I am not sure how to do it

A: Consider the given vector-valued function

Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

A: Click to see the answer

Q: Given the equation below, find dy dz 24r* + 3a"y + y* = 28 dy da Now, find the equation of the tange...

A: Given:

Q: can someone help me understand how to do this problem about triple integrals?

A: Given integral is eb=valuated as follows.

Q: prove

A: Click to see the answer

Q: A 105-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wi...

A: Click to see the answer

Q: Given g(x) = x^3 − 27x , use the first derivative test to determine the intervals on which the funct...

A: Click to see the answer

Q: Use the factorization s4 + 4a* = (s² – 2as + 2a²)(s² + 2as + 2a?) to derive the inverse Laplace tran...

A: Click to see the answer

Q: Write the given system in the form x' = tx - et y  + cos t, y' = e-t x + t2y - sin t

A: Click to see the answer

Q: for the quadratic function f(x)=x^2-2x-15 c) sketch f

A: Click to see the answer

Q: A perfect cube with a side length s has a volume of 64 cubic feet. The equation s3=64 shows the volu...

A: Click to see the answer

Q: A table of values of an increasing functions f is shown. х f(x) -87 10 -65 20 -27 30 25 40 45 50 63 ...

A: We will make use of Reimann left sum for the lower limit and Reimann right sum for the upper estimat...

Q: suppose the supply of x Units of a certain product at price p dollars Per unit is given by p=19+6In(...

A: Supply of x Units of a certain product at price p dollars Per unit is given by p = 19+6In(3x+1) For ...

Q: The line tangent to the graph of f at x=3 is y=4x-2 and the line tangent to the graph of g at x=3 is...

A: Given

Q: Find x correct to one decimal place. 30 y= 25

A: Click to see the answer

Q: Find all solutions of the equation. 4 sin x cos x+2 sin x +2 cos x +1 = 0

A: We factor the given expression by the factor by grouping  

Q: For the Attached problem use a calculator or computer system to calculate the eigenvalues and eigenv...

A: Click to see the answer

Q: dy 3. (A) Find for the following. dx (a) x = 5 sin 6t + 4 and y = 5 cos 6t + 3 (use parametric diffe...

A: Click to see the answer

Q: find directly the Laplace trans- forms of the functions described (by formula or graph) in Prob- lem...

A: Click to see the answer

Q: Evaluate the indefinite integral. (Use C for the constant of integration.)   etan(38x) sec2(38x...

A: Click to see the answer

Q: Please provide me with the answer and solutions.

A: Click to see the answer

Q: Scos“ x- sin' xdx x•sin³ xdx 3

A: Click to see the answer

Q: Ian boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revoluti...

A: Click to see the answer

Q: Apply the convolution theorem to find the inverse Laplace transforms of the functions in Problems 9....

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. If an an...

A: Click to see the answer

Q: Problem 49

A: The given integral is 

Q: State the domain, the range, and the intervals on which the function below is increasing decreasing,...

A: Domain is all possible values of x.  In the graph, x is from -7 to 12 So the domain is [-7,12].  The...

Q: Determine all points of discontinuity (if any) for the following functions: 5t x+4 a. f(x) = b. g(x)...

A: Click to see the answer

Q: cosx + + sin x 3

A: Click to see the answer

Q: Use power series to solve y' = 2y, y(0) = 5. %3D

A: Click to see the answer

Q: for the function f(x)= sqrt(x)/x-2 b) for what value of x is f(x)=1 ?

A: f(x) = √x/(x - 2) We have to find the value of x for which f(x) = 1  

Q: Evaluate x' -3 dx a.

A: Let the given function can be written as:

Q: ied region. on r = 4 + 2 sin e B) 367 - 16 4) C) 187 D) 367

A: Click to see the answer

Q: Consider the functions below and find an equation for the indicated composition. Then state the doma...

A: Click to see the answer

Q: Find f such that the given conditions are satisfied.   f primef′​(x)equals=xminus−55​, ​ f(44​)equa...

A: Click to see the answer

Q: Evaluate integral sin^4(x) dx

A: Click to see the answer

Q: find the Laplace transforms A preliminary in- of the functions in Problem. tegration by parts may be...

A: Click to see the answer

Q: Consider the function f(x) = Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(r)

A: Given :