Evaluate the Line Integral Over the Given Curve $C$

question 135

Short Answer

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

---

Definitions:

Smoking-Related Cancers

Cancers that are directly linked to tobacco use, including lung, throat, mouth, and bladder cancer.

Motor Coordination

The ability to execute smooth, accurate, and controlled motor responses, often involving the synchronization of movement and sensory feedback.

Addiction

Addiction is a chronic disorder characterized by compulsive engagement in rewarding stimuli, despite adverse consequences, often leading to physical and psychological dependence.

Depressant

A substance that reduces arousal or stimulation in various areas of the brain, often used to treat anxiety and sleep disorders.