$ \vec{F}=<x^{x^2},(x+z)\sin(y^3),(y^2-x^2+2yz)>$;C is the boundary of the triangular part of the plane $x+y+z=3$ that lies in the first octant

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I have a question which is following; $\vec{F}=\langle x^{x^2},(x+z)\sin(y^3),(y^2-x^2+2yz)\rangle$;C is the boundary of the triangular part of the plane $x+y+z=3$ that lies in the first octant.

I found the answer 9/2 , but the textbook doesn't give the answer for this question , so could someone solve this problem so that I can compare my answer with his/her's.