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Vector Calculus

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QuantumJG:
Hey guys,

I keep getting this question wrong.

Let a surface be paramaterised by

Φ(u,v) = (u-v,u+v,uv)

Let D be a unit disc (I'm assuming u2 + v2 1)

Find the area of Φ(D).

I keep getting whereas the answer is

/0:


What we want is

Now switching to polar works well:

QuantumJG:
I realized now where I stuffed up.

I did basically what you did, but after that to simplify things I let α = s2 + 2 but didn't change my terminals!

QuantumJG:
Another question:

F = (x-y,y-z,z-x)

Evaluate the surface integral of F if the surface S is the closed region:

x2 + y2 z 1 & x 0

Using the divergence theorem my answer was whereas the answer is

/0:
In cylindrical coordinates, ,

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