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:

Direct Materials Price Variance

The difference between the actual cost of direct materials used in production and the expected (or standard) cost.

Actual Costs

The genuine expenses that are incurred in the production or acquisition of goods and services.

Standard Costs

Predetermined cost estimates relating to how much it should cost to produce a product or provide a service under normal conditions.

Time Variance

The difference between the projected time to complete a task and the actual time taken, often analyzed in project management.