Hello, I am having problems with a question.. could someone tell me if im on the

ID: 3012017 • Letter: H

Question

Hello, I am having problems with a question.. could someone tell me if im on the right track

Question:

Let S be the boundary of the region enclosed by the paraboloid z = 4 - x2 - y2 and the plane z = 0 and let F(x,y,z) = x2i - 2xyj + x2zk

Evaluate the surface integral.

My solution:

I parameterize the equation for u and v such that x = u and y = v

Therefore z = 4 - u2 -v2

I also think that u and v need to be between -2 and 2, is that correct?

Then if I take the cross product of the partial derivatives of r(u,v) I get:

ru x rv = 2ui + 2vj + 1k

Then if i put it all into one surface integral equation i get

Surface integral = 2u3 - 4uv2 + 4u2-u4-u2v2

Do I evaluate that across u and v between -2 and 2??? because this solution seems to be not correct so far

Yes. you are on the right track, just evaluate the last expresion found under the limitss -2 to 2.

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