Trouble Finding Limits of Line Integrals

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Hckyplayer8

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Hello. I have very little natural mathematical ingenuity. Its something I've been working on. My method for passing this subject has to been to practice till I'm blue in the face. That brings us to line integrals. How am I suppose to look at a problem and instantly know how to solve and setup my limits?

For example "Sketch the solid described by x^2+y^2 is less than or equal to z is less than or equal to 1. Use the divergence theorem to evaluate the surface integral over the boundary of that solid of the vector field F=<y,z,xz>.

I got the partials down and I understand x^2+y^2 is the equation of a circle, so the cylindrical coordinate system is optimum. I also understand the limits for theta would be 2pi and 0.
 
Not sure what you mean by "Line Integrals".
What do you know about the divergence theorem?
 
blamocur said:
Not sure what you mean by "Line Integrals".
What do you know about the divergence theorem?
Click to expand...
Whoops. I meant surface integral. I would edit the post for the correction, but don't see an edit button.

After I find the partials I can take the triple integral of the solid to find the answer.

So the partials ends up just being x and x is equal to r cos(theta). Limits of a circle would be 0 to 2pi. But how do I find the limits of the two other dimensions?
 
Hckyplayer8 said:
I got the partials down and I understand x^2+y^2 is the equation of a circle
Click to expand...
Sorry but x^2+y^2 is NOT the equation of a circle. In fact, x^2+y^2 is not even an equation. Until you realize that, visualizing the 3-d graph will not be possible.

What does x^2+y^2 equal and how does that have any effect on the graph?
 
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Hckyplayer8 said:
Whoops. I meant surface integral. I would edit the post for the correction, but don't see an edit button.

After I find the partials I can take the triple integral of the solid to find the answer.

So the partials ends up just being x and x is equal to r cos(theta). Limits of a circle would be 0 to 2pi. But how do I find the limits of the two other dimensions?
Click to expand...
You say I have very little natural mathematical ingenuity. Its something I've been working on. Most everyone has to work on their math ingenuity.
To get better at this you should start off by saying complete thoughts and not by saying partials ends up just being x and x is equal to r cos(theta). Say which partials!
Being clear in your own mind about what is going on is key in building mathematical maturity.
 
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