XZ 7. Use divergence the reom to calculate the surface integral Sss Fods F = 1rr,...
6.) Use the Divergence theorom to evaluate the surface integral Sts Fods for the given vector field F and the oriented surface S. For closed surfaces, use the positive lost ward) orientation, F(x, y, z) = -xi - y jt zh, s is the part of 2 = x²ty² under the planes 2 = 4 with up ward orientation.
Use the Divergence Theorem to calculate the surface integral
F
· dS;
that is, calculate the flux of F across
S.
F(x, y,
z) = (6x3 +
y3)i +
(y3 +
z3)j +
15y2zk,
S is the surface of the solid bounded by the
paraboloid
z = 1 − x2 −
y2
and the xy-plane.
S
Let F(x,y,z) =( x3z)I+(y3z-yz3)j+z4k use the divergence theorem to calculate ∫∫cF•ds, that is , calculate flux of F across S, where S is the surface of the solid bounded by the hemisphere z = √ 2 - x2 - y2 and the xy - plane .
Use the Divergence Theorem to calculate the surface integral ∫∫SF·dS; that is, calculate the flux of F across S. F(x, y, 2) = eytan(z)i + y√(3 - x2)j + x sin(y) k, S is the surface of the solid that lies above the xy-plane and below the surface z = 2 -x4-y4 , -1 ≤ x ≤ 1, -1 ≤ y ≤ 1
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,...
ssignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you sut ssignment Scoring Your last submission is used for your score. 0/3 points | Previous Answers SCalcCC4 13.8.014 Use the Divergence Theorem to calculate the surface integral frs F·ds, that is, calculate the n 1. F r/Irl, where r xi yj+zk S consists of the hemisphere V 81- 2 and the disk x2+y2 S 81 in...
Evaluate the integral.
3. Sss (xz – yz)ds; where S is portion of the plane in R3 z = x + y + 2, that lies inside the cylinder x2 + y2 = 1.
Evaluate SS Fods where F= xi + 15 + 2 zk and s is the portion of Surface 2=1-x2 - y2 above the xy plane with upwards orientation the
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
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.