Math 224 3. Calculate le ayz dS where S is the part of the cone parametrized by 0sus1,0svs r(u, v)(ucos v, usin v, u),
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(,y,) dS, where f(,y,) = z'yz2 and S is the part ys 4 1. Parametrize, but do not evaluate, +y of the graph of...
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...
4. Evaluate Sl y(+12) ds, where S = {(1,y,z) : 2 = 4 – r?,05152,0 <ys...
4. Evaluate Sl y(+12) ds, where S = {(1,y,z) : 2 = 4 – r?,05152,0 <ys 5).
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk,...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Evaluate the following integral, ∫ ∫ S z dS, where S is the part of the...
Evaluate the following integral,
∫ ∫ S z dS, where S is the part of the sphere x2 + y2 + z2 = 16
that lies above the cone z = √ 3 √ x2 + y2 .
Problem #6: Evaluate the following integral where S is the part of the sphere x2+y2 + z -y2 16 that lies above the cone z = 3Vx+ Enter your answer symbolically, as in these examples pi/4 Problem #6:
Problem #6: Evaluate the...
Evaluate the integral for the following data. F = [x - z, y - x,z-y], 5....
Evaluate the integral for the following data. F = [x - z, y - x,z-y], 5. r= [ucos(v), usin(v), u), osus6, 0SVSH F.ndA=
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 ab...
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
can you show me the work for 2,3,4,5, thank you 2. Evaluate ff curl F n...
can you show me the work for 2,3,4,5, thank you
2. Evaluate ff curl F n dS, where F = (a2yz, yz2, 23e#v), and S is the part of the sphere a2 + y2+225 that lies above the plane z 1, oriented upwards. - Solution: -4T 3. A metal sheet is bent into the shape of the parabaloid r = y2+ 2 where 0 (r, y, z) is 6(x, y, z) = z. Find the mass of the resulting metal...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first oc...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
10. Evaluate the integral le z ds, where S is given by r(u, v) = (u...
10. Evaluate the integral le z ds, where S is given by r(u, v) = (u + v)i + (u – v)j + sin v k, Osus2, 0505
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...
4. Evaluate Sl y(+12) ds, where S = {(1,y,z) : 2 = 4 – r?,05152,0 <ys 5).
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
Evaluate the following integral,
∫ ∫ S z dS, where S is the part of the sphere x2 + y2 + z2 = 16
that lies above the cone z = √ 3 √ x2 + y2 .
Problem #6: Evaluate the following integral where S is the part of the sphere x2+y2 + z -y2 16 that lies above the cone z = 3Vx+ Enter your answer symbolically, as in these examples pi/4 Problem #6:
Problem #6: Evaluate the...
Evaluate the integral for the following data. F = [x - z, y - x,z-y], 5. r= [ucos(v), usin(v), u), osus6, 0SVSH F.ndA=
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
Evaluate the surface integral (x2 + y' +52 ) ds where S is the part of the cone z = 2- x2 + y2 above the z = 0 plane. The surface integral equals
can you show me the work for 2,3,4,5, thank you
2. Evaluate ff curl F n dS, where F = (a2yz, yz2, 23e#v), and S is the part of the sphere a2 + y2+225 that lies above the plane z 1, oriented upwards. - Solution: -4T 3. A metal sheet is bent into the shape of the parabaloid r = y2+ 2 where 0 (r, y, z) is 6(x, y, z) = z. Find the mass of the resulting metal...
5. Calculate the surface area of the portion of the sphere x2+y2+12-4 between the planes z-1 and z ะไ 6. Evaluate (xyz) dS, where S is the portion of the plane 2x+2y+z-2 that lies in the first octant. 7. Evaluate F. ds. a) F = yli + xzj-k through the cone z = VF+ア0s z 4 with normal pointing away from the z-axis. b) F-yi+xj+ek where S is the portion of the cylinder+y9, 0szs3, 0s r and O s y...
10. Evaluate the integral le z ds, where S is given by r(u, v) = (u + v)i + (u – v)j + sin v k, Osus2, 0505
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