Use Stokes' Theorem to Evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 21

Short Answer

Use Stokes' Theorem to evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$ . $\mathbf { F } ( x , y , z ) = 7 z \mathbf { i } + y \mathbf { j } + 4 x z \mathbf { k }$ ;
C is the boundary of the triangle with vertices $( 6,0,0 )$ , $( 0,6,0 )$ , and $( 0,0,6 )$ oriented in a counterclockwise direction when viewed from above

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Definitions:

Dendrites

Branch-like extensions of neurons that receive signals from other neurons.

Synapse

The junction between two neurons, where nerve impulses are transmitted from one neuron to another.

Endorphin

Neurotransmitters found in the brain that bind to opiate receptors and produce a feeling of pain relief and well-being.

Neurotransmitters

Chemical messengers that transmit signals across synapses from one neuron to another in the nervous system.