Use Green's Theorem to Find the Work Done by the Force

question 123

Multiple Choice

Use Green's Theorem to find the work done by the force
$$\mathbf { F } ( x , y ) = \left( 6 x - 7 y ^ { 2 } \right) \mathbf { i } + 3 y \mathbf { j }$$
in moving a particle in the positive direction once around the triangle with vertices $( 0,0 ) , ( 1,0 )$ , and $( 0,1 )$ .
Select the correct answer.

• A) 7
• B) \(\frac { 7 } { 6 }\)
• C) \(\frac { 7 } { 3 }\)
• D) 42

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Definitions:

Covariance

A measure that indicates the extent to which two variables change together, but does not indicate the strength of their relationship.

Independent

Not influenced by or dependent on another variable; in statistics, it often means that the occurrence of one event does not affect the probability of another event.

COV(X,Y)

Covariance between two variables X and Y, measuring the extent to which the variables change together and indicating the direction of their linear relationship.

Marginal Probability

The probability of occurring of a single event without consideration of any other events; it’s the likelihood of a single outcome.