(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. Evaluate [tex]\int_{S}\int curl F \cdot N dS[/tex] where S is the closed surface of the solid bounded by the graphs of x = 4, z = 9 - y^2, and the coordinate planes.

F(x,y,z) = (4xy + z^2)i + (2x^2 + 6y)j + 2xzk

2. Use Stokes's Theorem to evaluate [tex]\int_{C}F\cdot T dS[/tex]

F(x,y,z) = xyzi + yj +zk

S: 3x+4y+2z=12, first octant

2. Relevant equations

3. The attempt at a solution

1. For this one, I found the curl to be -6yi. However, I am at a loss as to how to get the N dS part without some sort of given equation for S? The book answer is 0.

2.

First I found the curl to be:

[tex]xyj - xzk[/tex]

I then used a theorem in my book to find N ds:

3/2i + 2j + k

Then I took the dot product:

[tex]<0, xy, -xz> \cdot <\frac{3}{2}, 2, 1> = 2xy - xz[/tex]

Integrating:

[tex]\int^{4}_{0}\int^{4-\frac{4y}{3}}_{0}(2xy-x(-\frac{3x}{2} - 2y + 6)*dx*dy [/tex]

which comes out to 64/27.

The book answer is 0.

Any pointers as to what I'm doing wrong would be appreciated.

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# Homework Help: Integrals with curl dot products

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