Use the Divergence Theorem to calculate the surface integral (fe F dS where F(x, y, z)= 6xzi+ 2y'j+(4z-3z2 k and S is the surface of the solid bounded by the paraboloid x =9-y2-z and the plane x = 5. O 384 n O -7,680 O 96 O -1,920 7

Q: Compute the flux of F¹ = 5(x + z)i + 5j + 5zk through the surface S given by y = x² + z², with 0 ≤ y…

A: The given surface is  and .The flux is given by  where  is the vector function that describes the…

Q: Consider the curve C between the points (1,0, 1) and (0, 1, 1) at the intersection of the cylinder…

A: To evaluate the line integral along with the curve c of ω=−ydx+xdy+dz.

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

A:

Q: Evaluate the surface integral , 2zds; o is the part of the following tetrahedron bounded by the…

A: We have to evaluate the surface integral ∬σ2zds where, σ is the part of the given tetrahedron…

Q: Evaluate the line integral faF · dr, where F(x, y, z) = -2xi – 5yj + 5zk and C is given by the…

A:

Q: Let I- (VxG) ndo, where G(x.y,z)=(ze*-y,4x,z*) and S is the part ofi the surface z=/x²+6y²+1 that…

A: Given that Gx,y,z=zex-y,4x,z4. The surfaces are given by z=x2+6y2+1⇒z2=x2+6y2+1 that lies inside the…

Q: Give a parameterization for the surface z F(u, v) = (u, v, ). x² - y²: = x

A: NOTE: Refresh your page if you can't see any equations. . the given surface is