Integrating Line Integrals over Ellipses

[shinobi12]

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

 

[jeffreydk]

What did you try already for a parametrization, etc?

 

[shinobi12]

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

 

[jeffreydk]

That would be the parametrization of the line y=x, but your curve that the line integral is over is the ellipse

$$4x^2+25y^2=100 \Rightarrow \text{ } \frac{2^2}{10^2}x^2+\frac{5^2}{10^2}y^2=1$$

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

$$x=\frac{10}{2}\cos{t} , y=\frac{10}{5}\sin{t}$$

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.