Understanding Line Integrals and Flux

What is the normal vector to a curve defined as in the context of line integrals involving flux?

• x prime, y prime

• y prime, negative x prime

• x prime, negative y prime

• negative y prime, x prime

How is flux defined in the context of line integrals?

• The measure of flow through a curve

• The measure of area under a curve

• The measure of distance along a curve

• The measure of volume around a curve

What is the role of the unit normal vector in the formula for flux?

• It points opposite to the curve

• It points to the right of the curve

• It points to the left of the curve

• It points along the curve

In the first example, what is the parameterization of the circle used for calculating flux?

• 5 cosine t, 5 sine t

• 2 cosine t, 2 sine t

• 4 cosine t, 4 sine t

• 3 cosine t, 3 sine t

What is the result of the flux calculation in the first example?

• 18 pi

• 9 pi

• 36 pi

• 27 pi

In the second example, why is the flux zero?

• The vector field is constant

• The vector field is zero

• The vector field is rotational

• The vector field is divergent

What is the vector field used in the second example?

• y, negative x

• negative y, x

• x, y

• negative x, negative y

In the third example, what is the nature of the vector field?

• Divergent

• Constant

• Convergent

• Radial

What is the result of the flux calculation in the third example?

• Negative 18 pi

• Positive 9 pi

• Zero

• Positive 18 pi

What does a negative flux indicate in the context of the third example?

• Outward flow

• Inward flow

• No flow

• Constant flow