# Parametrizing a Curve

1. Apr 29, 2013

### Karnage1993

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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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