Vs LEvaliutelFdS on surface sd fined byx' +y :4where F-x1+2: J + y k and banded...
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
04: Use a surface integral to find the outward flux of F = x i + y j + z k through the surface of the sphere za.
11. F (z, y, z)-(2c3 + уз) i + (уз + z3) j + 3уг z k, S is the surface of the solid bounded by the paraboloid z 1-2 -v2 and the zy-plane Answer 11. F (z, y, z)-(2c3 + уз) i + (уз + z3) j + 3уг z k, S is the surface of the solid bounded by the paraboloid z 1-2 -v2 and the zy-plane Answer
11. F (z, y, z)-(2c3 + уз) i + (уз...
e.g.4 Evaluate JJs F dS, where j + sin(zy)k and S is the surface of the region E bounded by the parabolic cylinder z- 1 a2 and the planes z-0,y-0, and y + z-2.
e.g.4 Evaluate JJs F dS, where j + sin(zy)k and S is the surface of the region E bounded by the parabolic cylinder z- 1 a2 and the planes z-0,y-0, and y + z-2.
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be the hemisphere 2 F(x, y,z)-yitj+3z k. Calculate JJs F dS, the flux of F across S
7. Find the surface area of the surface r(u, u) = u ui + (u + u)j + (u-u) k, u2 +02-1 V/16-x2-y2 with upward orientation and let 8. Let S be...
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...
Find the surface integral of the field F(x,y,z)= - i+2j+4 k across the rectangular surface z = 0, 0sxs2, Osys2 in the k direction The surface integral is (Type an exact answer, using a as needed.)
2 Suppose Vf(x, y, z) - 2xyze i ze* j + ye k. If f(0, 0, 0) 1, find f(2, 2, 3).
Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x> 0, y> 0 and z> 0 )j+ (3z + 7)k be the velocity field of a fluid. Let B be the Determine the flux of F through B in the direction of the outward unit normal
Let F(r, y, z)(z4+ 5y3)i + (y2 surface of the solid octant of the sphere x2+yj2 + 22 = 9 for x>...
Find the flux of the field F(x,y,z)=z² i +xj - 3z k outward through the surface cut from the parabolic cylinder z=1-yby the planes x = 0, x=2, and z=0. The flux is (Simplify your answer.)
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...