QuestionEvaluate the integral $I_{1}=\int_{L_{1}}(x+y) d x+(y-x) d y$ where $L_{1}$ is the path from $P(1,1)$ to $Q(2,2)$ via $S(1,2)$. $$I_{1}=$$

Studdy Solution
Sum the integrals from both segments to find the total integral $I_1$:
$$I_1 = \frac{1}{2} + \frac{7}{2} = \frac{8}{2} = 4$$
The value of the integral $I_1$ is:
$$\boxed{4}$$