Let C Be the Circle in Space with the Parameterization $\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { k } , \quad 0 \leq t \leq 2 \pi$

question 12

Essay

Let C be the circle in space with the parameterization $\vec { r } ( t ) = \cos t \vec { i } + \sin t \vec { k } , \quad 0 \leq t \leq 2 \pi$ Evaluate $\int_{C} \vec{F} \cdot d \vec{r}$ where $\vec { F } = 2 z e ^ { y ^ { 2 } } \vec { i } + \sin \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) \vec { j } + x \left( y ^ { 2 } - 1 \right) \vec { k }$

---

Definitions:

Aboriginal Population

The indigenous people who are the original inhabitants of a region, before the arrival of settlers or colonizers.

Population Size

The total number of individuals within a species in a specific area at a given time, influencing ecological dynamics and genetic diversity.

Growth Rate

An indicator of growth in size, quantity, value, or intensity during a specific timeframe.

Crude Birth Rate

The total number of live births per 1,000 population in a given year.