Parametrizing a Curve

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Homework Statement


Evaluate ##\int_{\gamma} F \ ds## where ##\gamma## is a parametrization of the curve of intersection of the surface ##z = x^4 + y^6## with the ellipsoid ##x^2 + 4y^2 + 9z^2 = 36## oriented in the counterclockwise direction when viewed from above.


Homework Equations





The Attempt at a Solution


The first thing I tried to do is plug the equation for the surface into the ellipsoid to get ##x^2 + 4y^2 + 9(x^4 + y^6)^2 = 36## which expands to ##9 x^8 + 18 x^4 y^6 + x^2 + 9 y^{12} + 4 y^2 = 36##. At this point, would I try to find the equation in terms of ##y##? Parametrizing this is where I seem to be stuck at.
 

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