Chapter 15 - Topics In Vector Calculus - 15.2 Line Integrals - Exercises Set 15.2 - Page 1108: 2

Result: a) \(2\) b) \(0\)

Step 1: a) \[ \int_C ds \] represents the length of the line segment, which is \(2\), since one coordinate is fixed, and the other changes by \(2\). Step 2: b) \[ \int_C e^{xy} dx = 0 \] due to the fact that \(x\) is constant on this segment, but since \(x\) is constant, then \({dx} = 0\). Result: a) \(2\) b) \(0\)