Evaluate the Line Integral Over the Given Curve $C$

question 26

Short Answer

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

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Definitions:

Operant Conditioning

A method of learning that occurs through rewards and punishments for behavior, encouraging the subject to associate certain behaviors with certain outcomes.

Responses

Reactions or answers provided following specific stimuli or situations.

Observational Learning

The process of learning behaviors by watching and imitating others, also known as modeling.

Responding

The act of reacting to a stimulus or situation, often measured in psychological experiments.