Finding parametrizattion for a Line Integral
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 parametrization x(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.