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

Correct Answer: 4.91

The correct Answers is :4.91 or 4.95 Approx