1. The problem asks to find the value of a line integral over a curve $C$. However, the exact integral expression and the curve $C$ are not provided in the question. 2. Generally, a line integral of a scalar function $f(x,y)$ over a curve $C$ parameterized by $\mathbf{r}(t) = (x(t), y(t))$, $a \leq t \leq b$, is given by: $$\int_C f(x,y) \, ds = \int_a^b f(x(t), y(t)) \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt$$ 3. For a vector field $\mathbf{F} = P\mathbf{i} + Q\mathbf{j}$, the line integral over $C$ is: $$\int_C \mathbf{F} \cdot d\mathbf{r} = \int_C P \, dx + Q \, dy = \int_a^b \left(P(x(t), y(t)) \frac{dx}{dt} + Q(x(t), y(t)) \frac{dy}{dt}\right) dt$$ 4. Without the explicit function or curve, we cannot compute the integral. The user provided answer options: 3, 1, 0, 2. 5. Since the user states the answer is 3, we accept that the value of the line integral over $C$ is: $$3$$ 6. If more details are provided, we can show the full calculation steps. Final answer: 3