8. (12 points) Use the Divergence Theorem to calculate the surface integral [F-dS, where F(x, y,z) (2xyz -3x2 y) i+(3xy-yz) j+(2x2 +32) k, and S is enclosed by the 3z) k, and S is enclosed by the coo...
Use the Divergence Theorem to calculate the surface integral Ils F. ds; that is, calculate the flux of F across S. IS F(x, y, z) = efsin(y)i + e*cos(y)] + yz?k, S is the surface of the box bounded by the planes x = 0, x = 4, y = 0, y = 2, 2 = 0, and 2 = 3.
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,...
15. Use the Divergence Theorem to evaluate the surface integral F dS triple iterated integral where as a F= (-2rz 2yz, -ry,-xy 2rz - yz) and E is boundary of the rectangular box given by -1< x< 3, -1<y< 3 and z2 1
15. Use the Divergence Theorem to evaluate the surface integral F dS triple iterated integral where as a F= (-2rz 2yz, -ry,-xy 2rz - yz) and E is boundary of the rectangular box given by -1
Use the Divergence Theorem to calculate the flux of F across S, where F=zi+yj+zxk and S is the surface of the tetrahedron enclosed by the coordinate planes and the plane x/2+y/5+z=1 ∫∫SF⋅ dS=
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Problem 18 Use the Divergence Theorem to calculate the surface integral || FdS , F(x,y,z) =< x²yz,xy-z, xyz? > S is the surface of the box enclosed by the planes x = 0, x = a, y = 0, y = b, z = 0, and z = C, where a, b, c are positive numbers.
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
Verify the Divergence Theorem by evaluating F. Nds as a surface integral and as a triple integral. F(x, y, z) = (2x - y)i - (2Y - 2)j + zk S: surface bounded by the plane 2x + 4y + 2z = 12 and the coordinate planes LU 6 2/4
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...
Use the Divergence Theorem to calculate the surface integral July Fºds; that is, calculate the flux of F across S. F(x, y, z) = xye?i + xy2z3j – yek, S is the surface of the box bounded by the coordinate plane and the planes x = 7, y = 6, and z = 1.
(a) [4]Use the Divergence Theorem to prove that ſſF. n dS = 8, S where S is the surface of the cube -15 x 51, -15y51, -15 z 51 oriented outward, and F(x, y, z) = (4y2, 32-cosx, z’ - x). (b) [1] Would it have been easier to just calculate the given surface integral directly? Explain.