Evaluate the Line Integral Over the Given Curve C $\int _ { C } 3 y ^ { 2 } z d s$

question 133

Multiple Choice

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

• A) \(- \frac { 1 } { 7 }\) \(\sqrt { 149 }\)
• B) 3
• C) 1
• D) \(\frac { \sqrt { 149 } } { 7 } \pi\)

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Definitions:

Saturated Fatty Acid

A type of fatty acid in which the hydrocarbon chain contains no double bonds, making it fully saturated with hydrogen atoms.

Lecithin

A fatty substance found in animal and plant tissues, widely used as an emulsifier in food products, cosmetics, and pharmaceuticals.

Triglyceride

A type of fat (lipid) found in your blood, made up of a glycerol backbone attached to three fatty acid chains, the main form of fat stored by the body.

Wax

A diverse class of organic compounds that are malleable at slightly higher than room temperature, consisting mostly of hydrocarbons or esters of fatty acids.