Is this legal in math? (calc 3)

[MetalManuel]

Homework Statement

I got a quiz back today, and i disagree with a lot of the things that my professor graded, but this one really made me upset.

(direct link, some can't see http://forum.bodybuilding.com/attachment.php?attachmentid=3329041&d=1304709473)

Homework Equations

What happened there was that I did this: (direct link, some can't see image for some reason http://forum.bodybuilding.com/attachment.php?attachmentid=3329051&d=1304710315)

Am I wrong? If not, what is this property called?

The Attempt at a Solution

 

[Pengwuino]

I have no idea what is going on in the problem. Can you re-write it so we can see what you're doing?

 

[MetalManuel]

I have no idea what is going on in the problem. Can you re-write it so we can see what you're doing?

Just look at the second image, that's basically what I did.

 

[flyingpig]

Just look at the second image, that's basically what I did.

What second image? There is only one image

 

[MetalManuel]

What second image? There is only one image

http://forum.bodybuilding.com/attachment.php?attachmentid=3329051&d=1304710315
I can see both (the image is hosted on another forum i go to)

 

[Pengwuino]

What you did in your second image is legal, but the problem appears to be a line integral. In the line integral, your parametrization is going to make it such that it is impossible to wind up with 3 integrals that can actually be combined like that.

When you actually make the parametrizations such that $$x = 2t, y=2t$$ for the first integral and then $$x=2-t, y=2$$ for the second integral, you must deal with the integrals separately. By making those substitutions, you actually have to replace your 'x' and 'y' variables with those new variables and do the integration over 'dt'. So you can't simultaneously make the substitutions $$x = 2t, y=2t$$ and $$x=2-t, y=2$$, you have to do one at a time and integrate one at a time.

 

[MetalManuel]

What you did in your second image is legal, but the problem appears to be a line integral. In the line integral, your parametrization is going to make it such that it is impossible to wind up with 3 integrals that can actually be combined like that.

When you actually make the parametrizations such that $$x = 2t, y=2t$$ for the first integral and then $$x=2-t, y=2$$ for the second integral, you must deal with the integrals separately. By making those substitutions, you actually have to replace your 'x' and 'y' variables with those new variables and do the integration over 'dt'. So you can't simultaneously make the substitutions $$x = 2t, y=2t$$ and $$x=2-t, y=2$$, you have to do one at a time and integrate one at a time.

IF they all have the same bounds, why does it matter if you do them all at once, or all separately? I would understand if my parameters were different but i did them all from 0 to 1 on purpose.

 

[Sethric]

Technically, it looks fine, since you just skip a step and decide to combine the three integrals. You actually parametrized the curve, had three integrals that had the same bounds and variable, and then grouped them. The fact that you didn't explicitly show that might be misleading, but as a grader, I would be fine with it.

As a side note, that is some of the most obscene grading I have ever seen. Tone it down a bit, jeez.

 

[Pengwuino]

Ah I see what's going on here. I couldn't make out the boxed area was an integral.

Yes what you did is okay, but as you said it only works if the bounds are the same.