Question

In: Math

Evaluate the surface integral. S x2yz dS, S is the part of the plane z =...

Evaluate the surface integral.

S

x2yz dS, S is the part of the plane

z = 1 + 2x + 3y

that lies above the rectangle

[0, 3] × [0, 2]

Solutions

Expert Solution

milcah answered 2 years ago
Next > < Previous

Related Solutions

Evaluate the surface integral. Double integral x dS, S is the triangular region with vertices (1,...
Evaluate the surface integral. Double integral x dS, S is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 6).
Evaluate the surface integral S F · dS for the given vector field F and the...
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) orientation. F(x, y, z) = xy i + yz j + zx k S is the part of the paraboloid z = 6 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has...
Evaluate the surface integral    S F · dS for the given vector field F and...
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) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 1 in the first octant, with orientation toward the origin
Evaluate the surface integral    S F · dS for the given vector field F and...
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) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 9 in the first octant, with orientation toward the origin
Evaluate the surface integral    S F · dS  for the given vector field F and the...
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) orientation. F(x, y, z) = xzey i − xzey j + z k S is the part of the plane x + y + z = 3 in the first octant and has downward orientation
Evaluate the surface integral    S F · dS for the given vector field F and...
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) orientation. F(x, y, z) = x i + y j + z4 k S is the part of the cone z = x2 + y2 beneath the plane z = 1 with downward orientation
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is...
Evaluate the following integral, ∫ ∫ S (x2 + y2 + z2) dS, where S is the part of the cylinder x2 + y2  =  64 between the planes z  =  0 and z  =  7, together with its top and bottom disks.
Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate...
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) = x4i − x3z2j + 4xy2zk, S is the surface of the solid bounded by the cylinder x2 + y2 = 1 and the planes z = x + 8 and z = 0
Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV to find ∬SF⋅dS where F(x,y,z)=x^2i+y^2j+z^2k and S S is the surface...
Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV to find ∬SF⋅dS where F(x,y,z)=x^2i+y^2j+z^2k and S S is the surface of the solid bounded by x^2+y^2=9 , z = 0 , and z=6
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi...
Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + cos z j + (x2z + y2)k and S is the top half of the sphere x2 + y2 + z2 = 4. (Hint: Note that S is not a closed surface. First compute integrals over S1 and S2, where S1 is the disk x2 + y2 ≤ 4, oriented downward, and S2 = S1 ∪ S.)
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT