Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where
F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉
and CC is the circle x2+y2=9x2+y2=9 on the plane z=6z=6 having traversed counterclockwise orientation when viewed from above.
The line integral equals
Use Stoke's Theorem to evaluate ∫CF⋅dr∫CF⋅dr where F=〈e−6x−1yz,e−1y+1xz,e−5z〉F=〈e−6x−1yz,e−1y+1xz,e−5z〉 and CC is the circle x2+y2=9x2+y2=9 on the...
Use Stoke's Theorem to evaluate ScF. dr, where F(x, y, z) = -xzzi + y2zj + zºk and C is the curve of intersection of the planez = 1 – X – Y and the cylinder x2 + y2 = 1, oriented counterclockwise as viewed from above.
Problem #8: Use Stokes' Theorem to evaluate F. dr where F = (x + 5z) i + (6x + y)j + (9y – =) k and C is the curve of JC intersection of the plane x + 2y += = 8 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) Problem #8:
4. Use Stokes' Theorem to evaluate F dr. F(x,y,z)-(3z,4x, 2y); C is the circle x2 + y2 4 in the xy-plane with a counterclockwise orientation looking down the positive z-axis. az az F dr-JI, (curl F) n ds and VGy, 1) Hint: use ax' dy
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = (-y+z)i + (x – z)j + (x – y)k. S is the surface z = V1 – 22 – y2, and C is the boundary of S with counterclockwise orientation (from above).
Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 3xzj + exyk, C is the circle x2 + y2 = 16, z = 8.
7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-< x2 sin(z), y2, xy >, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane. 7. (a) State Stoke's Theorem. (b) Use Stoke's theorem to evaluate curl(F)d where F(x, y, z)-, and s is the part of the paraboloid z = 1-2-1/2 that lies above the xy-plane.
Use Stokes' Theorem to evaluate the line integral $cF. dr, where F(x, y, z) = xyzi+yj + zk. S is the surface 3x + 4y + 2z = 12 in the first octant, and is the boundary of S with counterclockwise orientation (from above).
be = Use Green's Theorem to evaluate F. dr where F (3xy – esin x , 7x2 + Vy4 + 1) and C is the boundary of the region bounded by the circle x2 + y2 = 4 in the first quadrant with counterclockwise orientation.
Use Stokes's Theorem to evaluate F dr. In this case, C is oriented counterclockwise as viewed from above. S: the first-octant portion of x2 + z2 -64 over x2 + y2-64 Use Stokes's Theorem to evaluate F dr. In this case, C is oriented counterclockwise as viewed from above. S: the first-octant portion of x2 + z2 -64 over x2 + y2-64
Use Stokes' Theorem to evaluate ∫??⋅??∫CF⋅dr, where ?=−3?3?+3?3?+9?3?F=−3y3i+3x3j+9z3k and ?C is the intersection of the cylinder ?2+?2=1x2+y2=1 and the plane 3?+4?+?=63x+4y+z=6 (oriented counterclockwise as seen from above). ∫??⋅??=∫CF⋅dr=