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

This is a part of a bigger problem I am working on for my calculus 3 class. There is a parametric surface: [itex]^{\vec{}}r(u,v)=<u+v,u-v,1-2u>[/itex]

It represents the plane through points (1,0,0), (0,1,0) (0,0,1). As part of the problem, I need to set up a surface integral (specifically through this parametrization) and evaluate it. Now, what is the proper way of finding the upper and lower value for u and v?

2. Relevant equations

see above

3. The attempt at a solution

I tried plugging the values x,y and z from the above given points into the following system: [itex]^{}X(u,v)=u+v, Y(u,v)=u-v, Z(u,v)=1-2u[/itex]

As result, I obtained 3 pairs of u and v: [itex]^{}u=1/2,v=1/2 (for (1,0,0));u=0,v=0 (for (0,0,1)); u=1/2,v=-1/2 (for (0,1,0)) [/itex]

Is it mathematically correct to send the double integral over the parametric region for [itex]^{}u\epsilon[0,1/2][/itex] and [itex]^{}v\epsilon[-1/2,1/2] [/itex] ?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Parametric Surface

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