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Find for the given F and C

Find \(\int_{C} \vec{F} \cdot d r\) for the given \(\vec{F}\) and \(C\).

\(\cdot \vec{F}=-y \vec{i}+x \vec{j}+7 \vec{k}\) and \(C\) is the helix \(x=\cos t, y=\sin t r \quad z=t\), for \(0 \leq t \leq 2 \pi .\)

$$ \int_{C} \vec{F} \cdot d \vec{r}= $$


Find \(\int_{C} \overrightarrow{\mathrm{F}} \cdot d \overrightarrow{\mathrm{r}}\) for \(\overrightarrow{\mathrm{F}}=e^{y} \overrightarrow{\mathrm{i}}+\ln \left(x^{2}+1\right) \overrightarrow{\mathrm{j}}+\overrightarrow{\mathrm{k}}\) and \(C\), the circle of radius 4 centered at the origin in the \(y z\)-plane as shown below.

image.png

$$ \int_{C} \vec{F} \cdot d \vec{r}= $$

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