Find the Work Done by the Force Field $\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j }$

question 95

Multiple Choice

Find the work done by the force field $\mathbf { F } ( x , y ) = x \sin ( y ) \mathbf { i } + y \mathbf { j }$ on a particle that moves along the parabola $y = x ^ { 2 }$ from $( 1,1 )$ to $( 2,4 )$ .
Select the correct answer.

• A) \(\frac { ( 15 + \sin ( 1 ) - \sin ( 4 ) ) } { 2 }\)
• B) \(\frac { ( 17 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }\)
• C) \(\frac { ( 17 - \cos ( 1 ) + \cos ( 4 ) ) } { 2 }\)
• D) \(\frac { ( 15 + \sin ( 1 ) - \cos ( 4 ) ) } { 2 }\)
• E) \(\frac { ( 15 + \cos ( 1 ) - \cos ( 4 ) ) } { 2 }\)

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Definitions:

Monomers

Small, single molecules that can join with other similar molecules to form polymers through chemical reactions.

Complex Carbohydrates

Carbohydrates composed of sugar molecules linked together in long, complex chains, playing crucial roles in energy storage and structure.

Polysaccharide

A carbohydrate molecule composed of long chains of monosaccharide units bound together by glycosidic linkages.

Monosaccharides

Monosaccharides are the simplest form of carbohydrates consisting of a single sugar molecule, such as glucose and fructose.