calculating the line integral $\int_{L}|y|dl$

Question

I need help calculating the next line integral:

$\int_{L}|y|dl$ when $L:$ {$(x^2+y^2)^2=a^2(x^2-y^2)$}

I have no clue what info I can get from the equation so I haven't tried anything yet. a hint would be highly appreciated.

Answer 1

Hint:

$L$ is a lemniscate of Bernoulli, with parametric equations:

$$ x=\frac{a \cos t}{\sin^2 t+1} \qquad y=\frac{a \cos t \sin t}{\sin^2 t+1} $$

from this you can find $dl=\sqrt{dx^2+dy^2}$