Consider the vector field F(x, y) = 1 x+4 i + 1 3y+3 j in the first quadrant (x, y 0). The vectors i = (1, 0) and j = (0, 1) are the canonical basis vectors in R2 .

1) The path C is a straight line segment that connects the point (1, 0) to (2, 0). Calculate the value of the line integralcFdr along C.

2) Is F a conservative field on the domain {(x, y)| 2 x 2 and 1 y 4}?