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

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mattt9
 3 years ago
Best ResponseYou've already chosen the best response.1let 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 \[\sin(\sum_{i=4}^{14}\sum_{j=7}^{17} \int\limits_{C_ij}Fdotdr)\]

mattt9
 3 years ago
Best ResponseYou've already chosen the best response.1where dot is the dot operator not multiplication

mattt9
 3 years ago
Best ResponseYou've already chosen the best response.1and F is a vector field which should be in bold (or with an arrow on top), and dr is a vector as well

shaan_iitk
 3 years ago
Best ResponseYou've already chosen the best response.1okk 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.

mattt9
 3 years ago
Best ResponseYou've already chosen the best response.1Great! i'll give it a try tomorrow morning thank you

mattt9
 3 years ago
Best ResponseYou've already chosen the best response.1one question though, is there a way that I wouldn't have to integrate that 10 times? like do some terms automatically cancel out somehow?

shaan_iitk
 3 years ago
Best ResponseYou've already chosen the best response.1you 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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