Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...

Question

Question

Use Gauss's Divergence Theorem to evaluate JsFinds where F(x, y, z) = (x2 + cos(y2))i + (y-e)j + (22 +)k and S is the area limited by the cylinder + y2 = 4 and the plans +z=2, 2=0.

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

By divergene theoren. Is Finds = SSS div F du. divifis ( n + cos (923) + 1/3 ( 9 -2%) + 3 / ( 2 **) 20ty +27 7 2-n SSS div F

Please ask for any further clarifications. Please Upvote!!!

Add a comment

Answer 2

Similar Homework Help Questions

1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk....

1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk. Use the divergence thecrem to compute s F.ds where S is the portion of the cylinder x2 +y2-4 lying between z 1 and-2. 1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk. Use the divergence thecrem to compute s...
Use the Divergence Theorem to evaluate

Use the Divergence Theorem to evaluate \(\iint_{S} \mathbf{F} \cdot d \mathbf{S}\), where \(\mathbf{F}(x, y, z)=z^{2} x \mathbf{i}+\left(\frac{y^{3}}{3}+\cos z\right) \mathbf{j}+\left(x^{2} z+y^{2}\right) \mathbf{k}\) and \(S\) is the top half of the sphere \(x^{2}+y^{2}+z^{2}=4\). (Hint: Note that \(S\) is not a closed surface. First compute integrals over \(S_{1}\) and \(S_{2}\), where \(S_{1}\) is the disk \(x^{2}+y^{2} \leq 4\), oriented downward, and \(S_{2}=S_{1} \cup S\).)
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj +...

9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π 9. Let Q be the solid bounded by the cylinder x2 + y2...

Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is,...

Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is, calculate the flux of F across F(x,y,z) 3xy2 i xe7j + z3 k S is the surface of the solid bounded by the cylinder y2 + z2-4 and the planes x4 and x -4. Part 1 of 3 If the surface S has positive orientation and bounds the simple solid E, then the Divergence Theorem tells us that div F dV. For F(x, y,...
21. Use the divergence theorem to evaluate Sfs Fonds when F = y2xi + x2yj +...

21. Use the divergence theorem to evaluate Sfs Fonds when F = y2xi + x2yj + z²k, and when S is the complete surface of the region bounded by the cylinder x2 + y2 = 4 and by the planes 2 = O and z = 2.
6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 +...

6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 + y2 + z2 , yvx2 + y2 + z2 , z7 x2 + y2 + z2 ) and S consists of the hemisphere z V1 – x2 - y2 and the disk x2 + y2 = 1 in the xy-plane.

2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cyl...

2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cylinder E : r2 + y2 < 4, 0 2. (a) 9 pts] Evaluate F dS directly where S is the closed cylinder S which bounds E oriented outward. Note that S consists of three surfaces: S1 the surface of the cylinder x2 + y-4 for 0 z 2, the disc Di : x2 +92-4 which lies in the plane z 0 and...
Use Gauss's Divergence Theorem to calculate S S Funds ds F(x, y, z) = 3x i...

Use Gauss's Divergence Theorem to calculate S S Funds ds F(x, y, z) = 3x i + 2yj + 3z k. S is the solid sphere x 2 + y 2 + z 2 = 16 256 TT 512 1024 3 TT 2048 3 TT
to Problem #4: Use the divergence theorem find the outward flux SfFn Fºnds of the vector...

to Problem #4: Use the divergence theorem find the outward flux SfFn Fºnds of the vector field F = cos(2y + 3z)i + 10 ln(x2 + 2z)j + 3z2 k, where S is the surface of the region bounded within by the graphs of z = V25 – x2 - y2 , x2 + y2 = 9, and z = 0. + Problem #4: Enter your answer symbolically, as in these examples

Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, ...

Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, y + 2 tan(2), X22-1 and S is the top half of the sphere x2 +y2 25 Hint: S is not a closed surface. First compute integrals over S and S2, where Si is the disk x2 +y s 25, z 0 oriented downward and s,-sus, F-ds, = 滋 dy dx F.dS2 = S2 where X1 = 리= Z2 = IE F-ds, =...

Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...

Homework Answers

Add Answer to:
Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...

Post as a guest

Earn Coins

1, Evaluate Jsx2ds where s is the portion of the cylinder 22ヤU-9 lying between z-1 and 22. 2. Let F(, y, z)i+ j + zk....

Use the Divergence Theorem to evaluate

9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj +...

Tutorial Exercise Use the Divergence Theorem to calculate the surface integral ss F. ds; that is,...

21. Use the divergence theorem to evaluate Sfs Fonds when F = y2xi + x2yj +...

6. Use the Divergence Theorem to evaluate SSF. ds, where Ể(x, y, z) = (x/x2 +...

2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cyl...

Use Gauss's Divergence Theorem to calculate S S Funds ds F(x, y, z) = 3x i...

to Problem #4: Use the divergence theorem find the outward flux SfFn Fºnds of the vector...

Help Entering Answers (1 point) Use the Divergence Theorem to evaluate F . dS where F =くz2xHFz, ...

Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...

Homework Answers

Add Answer to: Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...

Post as a guest

Earn Coins

Add Answer to:
Use Gauss's Divergence Theorem to evaluate where and S is the area limited by the cylinder...