We're given that
[tex]\displaystyle \int_{C_1} f(x,y,z) \,ds = 43.1[/tex]
and
[tex]\displaystyle \int_{C_2} f(x,y,z) \,ds = -15.9[/tex]
The closed loop formed by joining C₁ and C₂ is then C₁ U (-C₂), which is to say we follow C₁ normally, then traverse C₂ in the opposite direction. Then
[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = \int_{C_1} f(x,y,z) \,ds + \int_{-C_2} f(x,y,z) \,ds[/tex]
[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = \int_{C_1} f(x,y,z) \,ds - \int_{C_2} f(x,y,z) \,ds[/tex]
[tex]\displaystyle \int_{C_1 \cup (-C_2)} f(x,y,z) \,ds = 43.1 - (-15.9) = \boxed{59}[/tex]
