Evaluate the Line Integral Over the Given Curve $C$

question 135

Short Answer

Evaluate the line integral over the given curve $C$ .
$$\int _ { C } 3 y ^ { 2 } z d s ; C : \mathbf { r } ( t ) = 10 t \mathbf { i } + \sin 7 t \mathbf { j } + \cos 7 t \mathbf { k } , 0 \leq t \leq \frac { \pi } { 2 }$$

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Definitions:

Whole Brain Death

A medical condition defined as the complete and irreversible cessation of all brain activity, used as a legal definition of death in many jurisdictions.

Cortex

The outer layer of the brain involved in numerous high-level functions including thought, memory, and decision making.

Brainstem

The lower part of the brain that connects the cerebrum with the spinal cord, responsible for regulating basic life functions such as breathing, heartbeat, and blood pressure.

Whole Brain Death

A medical and legal determination of death based on the irreversible cessation of all functions of the brain, including the brain stem.