- #1
clairez93
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Homework Statement
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
Homework Equations
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.