Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 24

Multiple Choice

Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ for the vector field F and the path C. (Hint: Show that F is conservative, and pick a simpler path.) $\mathbf { F } ( x , y ) = \left( 16 x ^ { 3 } y ^ { 2 } - 4 y \sin x \right) \mathbf { i } + \left( 8 x ^ { 4 } y + 4 \cos x \right) \mathbf { j }$ C: $\mathbf { r } ( t ) = ( 3 - \sin t ) \mathbf { i } + 2 \cos t \mathbf { j } ; \quad 0 \leq t \leq \pi$

• A) \(- 16 \cos ( 3 )\)
• B) 54
• C) 0
• D) 19

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Definitions:

Small Intestine

A long, coiled tube in the digestive system where most of the absorption of nutrients and minerals from food takes place.

Duodenum

The first section of the small intestine immediately beyond the stomach, which receives partially digested food from the stomach and begins the absorption of nutrients.

Jejunum

The middle section of the small intestine between the duodenum and ileum, where most of the nutrients from food are absorbed.

Ileum

The final and longest segment of the small intestine, important in the digestion and absorption of nutrients.