anonymous
  • anonymous
Are you familiar with line integrals in vector fields? if So please help with the question i post below
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
let C_ij be the boundary of the square [i,i+1]x[j,j+1], oriented clockwise, and \[F = .\] Calculate \[\sin(\sum_{i=4}^{14}\sum_{j=7}^{17} \int\limits_{C_ij}Fdotdr)\]
anonymous
  • anonymous
where dot is the dot operator not multiplication
anonymous
  • anonymous
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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anonymous
  • anonymous
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.
anonymous
  • anonymous
Great! i'll give it a try tomorrow morning thank you
anonymous
  • anonymous
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?
anonymous
  • anonymous
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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