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David and Sandra plan to evaluate line integral C F dr along a path in the xy - plane from ( 0 , 0 )

David and Sandra plan to evaluate line integral
C
F dr
along a path in the xy-plane from
(0,0) to (1,1).
The force field is
F(x, y)=(x +6y)i +(x + y2)j.
David chooses the path that runs along the x-axis from
(0,0) to (1,0)
and then runs along the vertical line
x =1
from
(1,0)
to the final point
(1,1).
Sandra chooses the direct path along the diagonal line
y = x
from
(0,0) to (1,1).
Whose line integral is larger?
DavidSandra
By how much?

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