Evaluate the Line Integral $\int _ { C } y d x - x d y$

question 34

Multiple Choice

Evaluate the line integral $\int _ { C } y d x - x d y$ along the circle $x = 2 \cos t , y = 3 \sin t , 0 \leq t \leq 2 \pi$ .

• A) \(0\)
• B) \(- 24 \pi\)
• C)\(- 6 \pi\)
• D) \(- 12 \pi\)
• E)\(- \frac { \pi } { 2 }\)
• F)\(24 \pi\)
• G)\(6 \pi\)
• H) \(12 \pi\)

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Definitions:

Probability

A numeric scale between 0 and 1 that quantifies how likely an event is to take place.

z

In statistics, 'z' typically refers to a z-score, a measure of how many standard deviations an element is from the mean.

Standard Normal Random Variable

A random variable that has a normal distribution with a mean of 0 and a standard deviation of 1.

P

Sometimes used as shorthand for "P-value," which assesses the strength of evidence against a null hypothesis in statistical testing.