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Are you familiar with line integrals in vector fields? if So please help with the question i post below

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let C_ij be the boundary of the square [i,i+1]x[j,j+1], oriented clockwise, and \[F = .\] Calculate \[\sin(\sum_{i=4}^{14}\sum_{j=7}^{17} \int\limits_{C_ij}Fdotdr)\]
where dot is the dot operator not multiplication
and F is a vector field which should be in bold (or with an arrow on top), and dr is a vector as well

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okk this is of the form \[\int\limits_{}^{} (x^2y^2+2 )dx + \int\limits_{}^{}(3x+y)dy\] .. Now apply greens theorem to get \[\int\limits_{j}^{j+1} \int\limits_{i}^{i+1}(3 - 2x^2y)dxdy\] ... solve this and use summation to find the value.
Great! i'll give it a try tomorrow morning thank you
one question though, is there a way that I wouldn't have to integrate that 10 times? like do some terms automatically cancel out somehow?
you don't need to integrate 10 times.. you need to integrate once ...Then you need to sum it 10 times (integration would give you number in terms of i and j)

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