Chapter 15 - Topics In Vector Calculus - 15.2 Line Integrals - Exercises Set 15.2 - Page 1108: 1

Result: a) \(1\) b) \(0\)

Step 1: a) \[ \int_C ds \] represents the length of the line segment, which is 1, since one coordinate is fixed and the other changes by 1. Step 2: b) \[ \int_C \sin(xy)\, dy \] This has to be 0 since \(\sin(xy) = 0\) along the given segment due to the fact that on this segment \(x = 0\). Result: a) 1 b) 0