Surface Integral Limits: Solving for u and v

[Woolyabyss]

Homework Statement

Problem is in image uploaded

Homework Equations

n/a

The Attempt at a Solution

x = u, y = v and z = 1 - u - v

∂r/∂u × ∂r/∂v = i + j + k
F dot N = u^2 + 3v^2

∫∫(u^2 + 3v^2 )dudv

My problem is I'm not sure what I should take as the limits?
Should I flip around the order of integration (dvdu) and have v go from 0 to 1-u and have u go from 0 to 1?

 

[LCKurtz]

Homework Statement

Problem is in image uploaded

Homework Equations

n/a

The Attempt at a Solution

x = u, y = v and z = 1 - u - v

∂r/∂u × ∂r/∂v = i + j + k
F dot N = u^2 + 3v^2

∫∫(u^2 + 3v^2 )dudv

My problem is I'm not sure what I should take as the limits?
Should I flip around the order of integration (dvdu) and have v go from 0 to 1-u and have u go from 0 to 1?

It doesn't matter which order you use for the integration. You have a triangle in the uv plane and you can do it either way. It isn't clear why your author changes the names of the variables from xy to uv instead of letting x and y just represent themselves. Set it up like you would any double integral.

 

[andrewkirk]

They have given you the limits in the problem, where they write $D=\{(u,v)\ :\ 0\leq u\ ...$. Have you tried using those? What did you get?