I've been asked to evaluate the line integral

$\displaystyle \int (10x^4 - 2xy^3)dx - 3x^2y^2dy $

Over the curve

$\displaystyle x^4 - 6xy^3 - 4y^2 = 0 $

Between the points (0,0) and (2,1).

What I'm trying to do is finding a parametrizationx(t) from the given curve and then put that into the integral so I can solve it.

However I can't seem to make it work. I tried solving x for y, so I can say x=t and y is a function of t. Or the other way round would work as well. But the crossterm $\displaystyle 6xy^3$ gets in the way. And the powers of both x and y aren't right to use the ABC formula.

Could anyone help me out on what to do here?

Thanks in advance

Edit: Apologies for the spelling mistake in the thread title. Can't edit it, it seems.

Edit 2: Got one sign in the integral wrong.