The answer for above problem is explained below.
Use Stokes's Theorem to calculate sį (curl F.nds F= (8 - y)i + (5 + x)j...
Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = zeli + x cos(y)j + xz sin(y)k, S is the hemisphere x2 + y2 + z2 = 4, y 2 0, oriented in the direction of the positive y-axis.
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper hemisphere x2 + y2 + z2 = 16 (z z 0) by the cylinder x2+ y2 =4 27)
Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction 27) F 3xi2xj + 7zk; C: the cap cut from the upper...
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =< x2,-y, z >, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in the xy plane.
6. (12pts) Use the divergence theorem to find the flux F.ndS with outward pointing normal n with F(x, y, z) =, where s is the surface of the hemisphere z = V 1-x2-y2 and its base in...
Question 5. Verify Stokes's Theorem for the field F(x, y, z) = 2z i+xj + y² k, where S is the surface of the paraboloid 2 = 4 – 22 - y2 and C is the curve of intersection of the paraboloid with the plane z = 0.
ie Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = x2 sin(z)i + y2 + xyk, S is the part of the paraboloid z = upward. - x2 - y2 that lies above the xy-plane, oriented
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = z2k through the upper hemisphere of the sphere x2 + y2 + z2 = 4, oriented away from the origin. If necessary, enter P as rho, 8 as theta, and o as phi. B D Flux IT do de А A= B= C = D= (b) Evaluate the integral. Flux = F.dĀ= SI S
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and y-x2 oriented in the positive direction
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and...
Let F(x,y,z) =( x3z)I+(y3z-yz3)j+z4k use the divergence theorem to calculate ∫∫cF•ds, that is , calculate flux of F across S, where S is the surface of the solid bounded by the hemisphere z = √ 2 - x2 - y2 and the xy - plane .
2. [25 pts) Let F(x, y, z) = x+i+ xyj + xzk be a vector field in space. Let S be the open surface z= 25 – x2 - y2, which is the upper hemisphere (or dome) of radius 5. Calculate the flux integral F.NDS