Question

Consider the line integral $\int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}$, where $\mathbf{F}(\mathbf{r}) = x \hat{\mathbf{i}} + y \hat{\mathbf{j}} + z \hat{\mathbf{k}}$, with $\hat{\mathbf{i}}, \hat{\mathbf{j}},$ and $\hat{\mathbf{k}}$ as unit vectors in the (x, y, z) Cartesian coordinate system. The path $C$ is given by $\mathbf{r}(t) = \cos(t) \hat{\mathbf{i}} + \sin(t) \hat{\mathbf{j}} + t \hat{\mathbf{k}}$, where $0 \leq t \leq \pi$. The value of the integral, rounded off to 2 decimal places, is _____

Answer 1

The correct Answers is :4.91 or 4.95 Approx