Flow chart for Line Integrals int_C vector F dot d vector r. The flow chart starts with the question: Is C a closed curve? Two arrows extend from this question, one for yes and one for no. The yes arrow points to the question: Is C in R^2? This question has 2 arrows. The yes arrow points to: Greens Theorem for Circulation. The no arrow points to: Stokes Theorem. Starting back at the question: Is C a closed curve? The no arrow points to the question: Is vector F conservative? Two arrows extend from this question, one for yes and one for no. The yes arrow points to: The Fundamental Theorem for Line Integrals, int_C vector F dot d vector r = int_C del f dot d vector r. The no arrow points to: Parameterize C and pull back to a one dimensional integral.