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Which theorem?

  • Thread starter duki
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  • #1
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Homework Statement



[tex]\int _c{(x^2 + y + \sqrt{x})dx + (y - x^2 + \sin{y}) dy[/tex]

Homework Equations



The Attempt at a Solution



I'm not sure which theorem to use here. Do I use Green's or the Divergence? Even once I get past this I'm not sure that I can get started.
 

Answers and Replies

  • #2
gabbagabbahey
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What curve are you supposed to integrate over?
 
  • #3
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Oops!

C is the curve transversed counterclockwise which is the boundary of the region bounded by the graphs of [tex] y = x^2 [/tex] and [tex] y = x^3 [/tex]
 
  • #4
gabbagabbahey
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Oops!

C is the curve transversed counterclockwise which is the boundary of the region bounded by the graphs of [tex] y = x^2 [/tex] and [tex] y = x^3 [/tex]
Parameterize that curve (you'll have to do it piecewise or separate it into two curves) and then follow the same procedure as in your previous path integral question...
 
  • #5
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The part I'm concerned about is the boundaries... How do I find those?
 
  • #6
gabbagabbahey
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Where does [itex]y=x^2[/itex] intersect [itex]y=x^3[/itex]?
 
  • #7
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0 and 1?
 
  • #8
gabbagabbahey
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Yep.:smile:....So draw your y=x^2 and y=x^3 graphs from x=0 to x=1 to get an idea of what your curve looks like. Then parameterize it and integrate.
 
  • #9
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Groovy.
 

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