Line integral: The integral of the field line F(x, y) = (ax+by, cx+dy), where a, b, c

[fredericoahb]

Dear all, i'm from Brasil and a i tried to translate the question that i cant solve. I dont know how to aplly the line integral along the curve. I sent the original question written in portuguese. Thanks.



The integral of the field line F(x, y) = (ax+by, cx+dy), where a, b, c and d are real constants, calculated over every single closed path C: [0, 1] -> R2, traveled once in the counterclockwise direction, has value equal to the area of the region enclosed by C. Under these conditions, we can conclude that:

a) c-b=1
b) d-a=1
c) b-c=1
d) a-d=1
e) a+b+c+d=0

 

[Deleted member 4993]

Dear all, i'm from Brasil and a i tried to translate the question that i cant solve. I dont know how to aplly the line integral along the curve. I sent the original question written in portuguese. Thanks.



The integral of the field line F(x, y) = (ax+by, cx+dy), where a, b, c and d are real constants, calculated over every single closed path C: [0, 1] -> R2, traveled once in the counterclockwise direction, has value equal to the area of the region enclosed by C. Under these conditions, we can conclude that:

a) c-b=1
b) d-a=1
c) b-c=1
d) a-d=1
e) a+b+c+d=0

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