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Evaluate the line integral \int_C \mathbf{F}\cdot d\mathbf{r}, where \mathbf{F}(x,y,z) = 4 \sin x \mathbf{i} + 2 \cos y \mathbf{j} + 5x z\mathbf{k} and C is given by the vector function \mathbf{r}(t) = t^3 \mathbf{i} - t^2 \mathbf{j} + t^1 \mathbf{k} , \quad 0 \le t \le 1.
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Evaluate the line integral \int_C \mathbf{F}\cdot d\mathbf{r}, where \mathbf{F}(x,y,z) = -3x\mathbf{i} + 3y\mathbf{j} - z\mathbf{k} and C is given by the vector function \mathbf{r}(t) = \langle \sin t, \cos t, t \rangle, \quad \ 0\le t \le 3\pi/2.
