(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

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540