We have a vector field F = (1+y, x+y, x) and a closed curve C made of

the union of three curves C = C₁ UC₂ UC3, with the three curves running

back to back, and parameterized by the equations respectively.

Answer the following questions:

1. Is this field F irrotational?

2. From the answer you gave to the question 1 above, can you tell without

doing any calculations, just using some theorems: what is the circula-

tion (path integral along the closed curve) of the vector field F along

C?

3. Calculate by evaluating the line integral along each of the three parameterized

curves. Find the numeric answer as a fraction, or similar numerical

expressions, and do not calculate it in decimal form.

Fig: 1

Fig: 2