Use Stokes Theorem to evaluate [F F. dr where F(x, y, z)=zi+yj+22² + y²)k and C is the boundary of the part of the paraboloid where z = 49-2²-y² which lies above the xy-plane and C is oriented counterclockwise when viewed from above.

Q: Solve the following 2nd order differential equations: d²y 2 dx2 dy (i) 11 + 12y = 3x – 2 dx - d²y 2…

A: Given differential equation is: 2y''-11y'+12y=3x-2 Auxiliary equation corresponding to differential…

Q: Calculate F· dS where F = (4x*z, 4y°z, 3:*) S is the surface of the solid bounded by the hemispheres…

A: Given

Q: F · dr  where F  =  (x + 5z) i  +  (7x + y) j  +  (2y − z) k   and C is the curve of intersection of…

A:

Q: F. dr where C is oriented counterclockwise as viewed from above. Jc F(x, y, z) = xyi + 3zj + 5yk,…

A:

Q: Let S be the portion of the plane 2x + 3y + z = 2 lying between the points (-1, 1, 1), (2, 1, −5),…

A: S is the portion of the plane 2x+3y+z=2 lying between the points (-1, 1, 1), (2, 1,-5), (2, 3,-11)…

Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: Consider the planes P₁: 3x+y-2zm 7 and P₂ : x+2y+z=4. Give a parametrization for the line of…

A:

Q: Let F = 2x3i + 2y3j + 2z3k and let S be the surface consisting of the hemisphere x2 + y2 + z2 = 1, z…

A: Given, F=2x3i+2y3j+2z3k and  S be the surface consisting of the hemisphere x2+y2+z2=1, z≥0 and the…

Q: Let F(x, y, z) = -3y² + 4z + 6æk and C is the curve of the intersection of the plane x + y + z = 2…

A:

Q: b) Use Gauss theorem to evaluate F.ndS, where F(r, y, 2) = (2x²y² + In z) i – xy³ j – tanh(a² + y³)…

A:

Q: Use Stokes' Theorem to evaluate F• dr where C is oriented counterclockwise as viewed from above.…

A: Here use the stokes theorem to find the integral of the function.  And given that the function…

Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

A:

Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: Let F = (y,3z + x,3y² ). Use Stokes' Theorem to find a plane with the equation ax + by + cz = 0…

A: step:- 1 Stock's Theorem:- ∮CF.dr=∫∫SF.n ds=∫∫DF.(rx×ry) dA; D is disk. Step:- 2 Given that   F=y2,…

Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: Evaluate F-di where F(x, y, z)=1li +(x+yz)j+(xy- Vz 3x+2y+z=6 in the first octant. C is a positively…

A: Here we have to evaluate ∫CF→·dr→=? Where F→(x,y,z)=i^+(x+yz)j^+(xy-z)k^ and C is the boundary of…

Q: Use Stokes' theorem to evaluate where = 3x²1+8x³yj + 3x²yk (V x F) - dA and S is the portion of the…

A: Given that S is the portion of the  plane that lies inside the box defined by the .

Q: Use Stokes' Theorem evaluate 4F.dr if to F(x, y,z)= xzi+ xyj+3xzk and C is the boundary of the…

A: