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