Evaluate the Line Integral $\begin{array} { l } \int _ { C } \mathbf { F } \cdot d \mathbf { r } ,\end{array}$

question 4

Multiple Choice

Evaluate the line integral $\begin{array} { l } \int _ { C } \mathbf { F } \cdot d \mathbf { r } ,\end{array}$ where $\mathbf { F } ( x , y ) = ( x - y ) \mathbf { i } + ( x y ) \mathbf { j }$ and C is the arc of the circle $x ^ { 2 } + y ^ { 2 } = 25$ traversed counterclockwise from ( $5$ , 0) to (0, - $5$ ) . Round your answer to two decimal places.

• A) \(90.07\)
• B) \(91.07\)
• C) \(92.07\)
• D) \(89.07\)
• E) \(88.07\)

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Definitions:

Temperature

A physical quantity expressing the subjective perceptions of hot and cold, measured by a thermometer.

Increased

A term denoting a situation or quantity that has grown or become larger or greater in size, volume, number, or degree.

Negatively Related

A term describing two variables that move in opposite directions, where an increase in one leads to a decrease in the other.

Slopes Downward

Describes a line or curve on a graph that decreases in value as it moves from left to right, indicating a negative relationship between two variables.