# Calculate the line Integral

1. Nov 18, 2008

### shinobi12

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. Nov 18, 2008

### jeffreydk

What did you try already for a parametrization, etc?

3. Nov 18, 2008

### 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

4. Nov 18, 2008

### 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.