Am I even supposed to do the integral?

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Homework Statement


I am to find the partial derivatives fxx, fxy, and fyy off(x,y)=
eq.latex?\int_{y^2}^{\sqrt{x}}cos(t^2)dt.gif
The integral from y squared to the square root of x of cos(t squared) dt

Accidentally posted, was editing to get the TEX to work

Homework Equations



The Attempt at a Solution



All rules of integration I know fail, and attempting to use an integral calculator leads me to a term "Fresnel", which has never before been explained in my class. This leads me to assume I'm not supposed to take the integral; how, then, do I account for sqrt(x) and y^2?
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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