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![Z=1542 312 li Area=s [[Z3J17+9z+] 41. dz Zo Area=113 j2=113 Cz! J1+12+] dz Z=o dk =z²dz (11) 36 Let k=14924 dk= 36 2² dz > 1](http://img.homeworklib.com/questions/d94ff7c0-4f85-11ec-aa79-5ffe1b4c1c84.png?x-oss-process=image/resize,w_560)
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(1 pt) Calculate S/sf(x, y, z) ds For 231 where 0...
Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0 < z, y < 101 ; JJs f(z, y,z) ds-...
Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0 < z, y < 101 ; JJs f(z, y,z) ds- f(z, y,z) = z
Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluat...
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal.
F-dS where S is the cylinder x? +-2, 0 s y
A B C Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3...
A
B
C
Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
S 6 Calculate the fleux SSF. ds, where I la, y, z)= <0? 2², 227 and...
S 6 Calculate the fleux SSF. ds, where I la, y, z)= <0? 2², 227 and S is the finite cylinder (with top and bottom) given by x² + y² = 1, 2 = 0, Z = 3,
Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x +...
Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x + y + z and o is the is the surface of the cube defined by the inequalities 0 < x < 5,0 Sy < 5 and 0 <3 < 5. [Hint: integrate over each face separately.] 1 f(x, y, z) ds =
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉 and SS is the top half of...
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where
F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉
and SS is the top half of the sphere x2+y2+z2=9x2+y2+z2=9.
(1 point) Use the Divergence Theorem to evaluate FdS where F2x +3 tan2).^z-1 and S is the top half of the sphere x2 +y2 + z2 -9 Hint: S is not a closed surface. First compute integrals overs, and S2 , where S, is the disk x2 + y2 < 9, z = 0 oriented downward and S2 = S U...
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...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
(x, y, z) dS for the following: (a) f(x, y, z) x+4 , where S is the portion of the generalized cy...
Please show all work. Answers provided below
Answers:
(x, y, z) dS for the following: (a) f(x, y, z) x+4 , where S is the portion of the generalized cylinder y2 +4z 16 cut off by the planesx 0, x-1 and z- 0 (b) f (c) f (x, y, z)-xyz, where S is the torus given in [12](e) (x, y, z)-xyz, where S is the portion of the cylinder y + z the planes x-1 and x 2 f(x, y,...
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...
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 coordinate planes and x+y+z = 6
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...
Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0 < z, y < 101 ; JJs f(z, y,z) ds- f(z, y,z) = z
Calculate JJs f(x, y,z) dS For Part of the surface z-z", where 0
F-dS where S is the cylinder x? +-2, 0 s y < 2 oriented by the unit normal 5- Let F(x,y,z)= (-6x,0,-62). Evaluate pointing out of the cylinder. 6-Let F(x, y,2)- yi- xj +zx°y?k. Evaluate (Vx F) . dS where S is the surface x2+y+32 - 1, z <0 oriented by the upward- pointing unit normal.
F-dS where S is the cylinder x? +-2, 0 s y
A
B
C
Parametrize, but do not evaluate, //f(x, y, z) ds, where f(x, y, z) 2y22 and S is the part , where J(,y,) 3 3 and 0 Sys4 of the graph of z2 over the rectangle -2 s . Parametrize, but do not evaluate, F.n ds, where F (,-,z) and S is the sphere of radius 2 centered at the origin. Calculate JJs xyz dS where S is the part of the cone parametrized by r(u, u) (ucos...
S 6 Calculate the fleux SSF. ds, where I la, y, z)= <0? 2², 227 and S is the finite cylinder (with top and bottom) given by x² + y² = 1, 2 = 0, Z = 3,
Evaluate the surface integral lis(r,y,z) (x, y, z) ds where f(x, y, z) = x + y + z and o is the is the surface of the cube defined by the inequalities 0 < x < 5,0 Sy < 5 and 0 <3 < 5. [Hint: integrate over each face separately.] 1 f(x, y, z) ds =
Use the Divergence Theorem to evaluate ∬SF⋅dS∬SF⋅dS where
F=〈z2x,y33+3tan(z),x2z−1〉F=〈z2x,y33+3tan(z),x2z−1〉
and SS is the top half of the sphere x2+y2+z2=9x2+y2+z2=9.
(1 point) Use the Divergence Theorem to evaluate FdS where F2x +3 tan2).^z-1 and S is the top half of the sphere x2 +y2 + z2 -9 Hint: S is not a closed surface. First compute integrals overs, and S2 , where S, is the disk x2 + y2 < 9, z = 0 oriented downward and S2 = S U...
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...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
Please show all work. Answers provided below
Answers:
(x, y, z) dS for the following: (a) f(x, y, z) x+4 , where S is the portion of the generalized cylinder y2 +4z 16 cut off by the planesx 0, x-1 and z- 0 (b) f (c) f (x, y, z)-xyz, where S is the torus given in [12](e) (x, y, z)-xyz, where S is the portion of the cylinder y + z the planes x-1 and x 2 f(x, y,...
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 coordinate planes and x+y+z = 6
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...
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