(1 point) use stokes' theorem to evaluate (v x f). ds where f(x, y, z) = -13yzi + 13xzj +4(x2 + y2)zk and s is the part of the paraboloid z = x2 + y2 that lies inside the cylinder x2 + y2 = 1, oriented upward. js

By using Stokes's theorem to the required (VxF).dS  is 26π.

Given that,

Function F(x, y, z) = -13yzi + 13xzj +4(x2 + y2)zk .

And S is the part of the paraboloid z = x2 + y2 that lies inside the cylinder x2 + y2 = 1, oriented upward. JS.

We have to determine,

Use Stokes' theorem to evaluate (V x F).dS.

According to the question,

By using Stokes's theorem to evaluate (V x F).dS .

F(x, y, z) = -13yzi + 13xzj +4(x2 + y2)zk .

Stokes' theorem says the integral of the curl of over F is s equal to the integral of F along the boundary of S , with counterclockwise orientation (when viewed from above).

This boundary is the circle set in the plane .

Then,

The parameterize path is given by the,

Then,

Hence, By using Stokes's theorem to the required (VxF).dS  is 26π.

To know more about Integration click the link given below.

Stokes' theorem equates the integral of across with the integral of along the boundary of , which is the intersection of the paraboloid and the cylinder , or the circle in the plane centered at (0, 0, 1) with radius 1.

Parameterize this intersection (call it ) by

with . Then

step-by-step explanation:

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