Suppose is the path given by for , is the path given by for , and . Without calculating the integrals, which of the following is true?
In the figure, the curve from to consists of two quarter-unit circles, one with center (1, 0) and the other with center (3, 0). Calculate the line integral , where .
Let be the arc of a unit circle in the -plane traversed counterclockwise from to . Determine the exact value of the line integral of the vector field over .