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

Question

anonymous · Answer

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 $$\sin(\sum_{i=4}^{14}\sum_{j=7}^{17} \int\limits_{C_ij}Fdotdr)$$

anonymous · Answer

where dot is the dot operator not multiplication

anonymous · Answer

and F is a vector field which should be in bold (or with an arrow on top), and dr is a vector as well

anonymous · Answer

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 · Answer

Great! i'll give it a try tomorrow morning
thank you

anonymous · Answer

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 · Answer

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)