Practice: Line Integrals & Green's

10 multiple choice · 4 free response · 1 walkthroughs

Q1.

basicLine Integrals T/F #2

True/False: Reversing the orientation of

C

flips the sign of

\int_{C} f d s

Q2.

basicLine Integrals T/F #4

True/False: Reversing the orientation of

C

leaves

\int_{C} F \cdot d r

unchanged.

Q3.

basicLine Integrals T/F #6

F

is conservative on

D

and

C

is a closed curve in

D

, then

\oint_{C} F \cdot d r

equals

Q4.

basic

Green's Theorem (circulation form) states

\oint_{C} P d x + Q d y =

Q5.

basic

True/False: Green's Theorem requires

C

to be a simple closed curve.

Q6.

intermediate

For

F

that is **tangent** to

C

at every point,

\int_{C} F \cdot d r

Q7.

intermediate

Area of a region

D

via Green's Theorem can be computed as

Q8.

basicLine Integrals T/F #8

Curl (

z

-component) of a 2D field measures

Q9.

intermediate

\int_{C} 2 x y d x + (x^{2} + y^{2}) d y

where

C

is the segment from

(0, 0)

(2, 1)

equals

Q10.

intermediateLine Integrals T/F #11

True/False: The flux form of Green's Theorem in the plane reads

\oint_{C} F \cdot d r = \iint_{D} \nabla \cdot F d A