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

Studdy Solution
Sum the results from both segments to find the total integral:
$$I_2 = \frac{5}{2} + \left(-\frac{1}{2}\right)$$ $$= \frac{5}{2} - \frac{1}{2}$$ $$= \frac{4}{2}$$ $$= 2$$
The value of the integral $I_2$ is:
$$\boxed{2}$$