## mattt9 3 years ago Are you familiar with line integrals in vector fields? if So please help with the question i post below

1. mattt9

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. mattt9

where dot is the dot operator not multiplication

3. mattt9

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

4. shaan_iitk

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.

5. mattt9

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

6. mattt9

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?

7. shaan_iitk

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)