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Let gamma be given on 0<u<1 by (x,y)=(1-u,u) The vector field (F1,F2) is a gradient field.
Integral over gamma of Fdx+F2dy Where:
F1 = x*y^2
F2 = x^2*y
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The solution is attached below in two files. the files are identical in content, only ...
The 4-pages long file includes a detailed solution of the problem using the fundamental theorem of calculus.