Calculate the line Integral

  • Thread starter shinobi12
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  • #1
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Homework Statement


Calculate the anti-derivative of ydx where c in the ellipse 4x^2 + 25y^2 = 100


Homework Equations


Definition of a line integral


The Attempt at a Solution


I tried parameterizing the equations but I sure if am making the right choice
 

Answers and Replies

  • #2
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What did you try already for a parametrization, etc?
 
  • #3
16
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I assumed we had a line from (0,0) to (1,1) so we had a vector of <1,1> so...
x=t
y=t
 
  • #4
135
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That would be the parametrization of the line y=x, but your curve that the line integral is over is the ellipse

[tex]4x^2+25y^2=100 \Rightarrow \text{ } \frac{2^2}{10^2}x^2+\frac{5^2}{10^2}y^2=1[/tex]

I wrote it in a more suggestive way; can you see why the parametrization should be the following?

[tex] x=\frac{10}{2}\cos{t} , y=\frac{10}{5}\sin{t}[/tex]

Think of the parametrization of a circle and why that works if it doesn't make sense. Now try to see what you get for the line integral.
 

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