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

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mattt9Best ResponseYou've already chosen the best response.1
let C_ij be the boundary of the square [i,i+1]x[j,j+1], oriented clockwise, and \[F = <x^2y^2+2, 3x+y>.\] Calculate \[\sin(\sum_{i=4}^{14}\sum_{j=7}^{17} \int\limits_{C_ij}Fdotdr)\]
 2 years ago

mattt9Best ResponseYou've already chosen the best response.1
where dot is the dot operator not multiplication
 2 years ago

mattt9Best ResponseYou've already chosen the best response.1
and F is a vector field which should be in bold (or with an arrow on top), and dr is a vector as well
 2 years ago

shaan_iitkBest ResponseYou've already chosen the best response.1
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.
 2 years ago

mattt9Best ResponseYou've already chosen the best response.1
Great! i'll give it a try tomorrow morning thank you
 2 years ago

mattt9Best ResponseYou've already chosen the best response.1
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?
 2 years ago

shaan_iitkBest ResponseYou've already chosen the best response.1
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)
 2 years ago
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