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Calculate the line Integral

  1. Nov 18, 2008 #1
    1. The problem statement, all variables and given/known data
    Calculate the anti-derivative of ydx where c in the ellipse 4x^2 + 25y^2 = 100


    2. Relevant equations
    Definition of a line integral


    3. The attempt at a solution
    I tried parameterizing the equations but I sure if am making the right choice
     
  2. jcsd
  3. Nov 18, 2008 #2
    What did you try already for a parametrization, etc?
     
  4. Nov 18, 2008 #3
    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
     
  5. Nov 18, 2008 #4
    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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