Mathematics

Current Score : – / 0 Due : Wednesday, November 19 2014 04:00 PM CST

1. –/0 pointsSEssCalcET2 13.2.002.

Evaluate the line integral, where C is the given curve.

2. –/0 pointsSEssCalcET2 13.2.003.MI.SA.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise Evaluate the line integral, where C is the given curve.

is the right half of the circle x2 + y2 = 25 oriented counterclockwise

3. –/0 pointsSEssCalcET2 13.2.007.

Evaluate the line integral, where C is the given curve.

C consists of line segments from (0, 0) to (5, 1) and from (5, 1)

to (6, 0)

Review Problems for Test #2 (Homework)

Rustom Hamouri Math 344, section 11795, Fall 2014 Instructor: Buma Fridman

WebAssign

xy ds, C: x = t2, y = 2t, 0 ≤ t ≤ 1

C

xy4 ds, C

C

(x + 5y) dx + x2 dy,

C

4. –/0 pointsSEssCalcET2 13.2.010.

Evaluate the line integral, where C is the given curve.

is the line segment from

5. –/0 pointsSEssCalcET2 13.2.020.

Evaluate the line integral where C is given by the vector function r(t).

6. –/0 pointsSEssCalcET2 13.3.004.

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. If it is not, enter NONE.

f(x, y) = + K

xyz2 ds, C

C (−2, 6, 0) to (0, 7, 1)

F · dr,

C

F(x, y, z) = (x + y)i + (y − z)j + z3k

r(t) = t2 i + t3 j + t2 k, 0 ≤ t ≤ 1

F(x, y) = ex sin y i + ex cos y j

7. –/0 pointsSEssCalcET2 13.3.005.

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. If it is not, enter NONE.

f(x, y) = + K

8. –/0 pointsSEssCalcET2 13.3.011.

Consider F and C below.

(a) Find a function f such that F = ∇f.

(b) Use part (a) to evaluate along the given curve C.

F(x, y) = ex cos y i + ex sin y j

F(x, y) = 4xy2 i + 4x2y j

C: r(t) = t + sin πt, t + cos πt , 0 ≤ t ≤ 11 2

1 2

f(x, y) =

∇f · dr

C

9. –/0 pointsSEssCalcET2 13.3.015.

Consider F and C below.

(a) Find a function f such that F = ∇f.

(b) Use part (a) to evaluate along the given curve C.

10.–/0 pointsSEssCalcET2 13.3.020.

Find the work done by the force field F in moving an object from P to Q.

11.–/0 pointsSEssCalcET2 13.3.029.

Determine whether or not the given set is open, connected, and simply-connected. (Select all that apply.)

open

connected

simply-connected

F(x, y, z) = yzexzi + exzj + xyexzk, C: r(t) = (t2 + 3)i + (t2 − 4)j + (t2 − 5t)k, 0 ≤ t ≤ 5

f(x, y, z) =

F · dr

C

F(x, y) = e−y i − xe−y j

P(0, 2), Q(3, 0)

(x, y) | 9 ≤ x2 + y2 ≤ 16, y ≥ 0

12.–/0 pointsSEssCalcET2 13.4.506.XP.

Use Green’s Theorem to evaluate (Check the orientation of the curve before applying

the theorem.)

13.–/0 pointsSEssCalcET2 13.4.001.MI.

Evaluate the line integral by the two following methods.

C is counterclockwise around the circle with center the origin and radius 7

(a) directly

(b) using Green’s Theorem

F · dr.

C

F(x, y) = e2x + x2y, e2y − xy2

C is the circle x2 + y2 = 1 oriented clockwise

(x − y) dx + (x + y) dy

14.–/0 pointsSEssCalcET2 13.4.003.

Evaluate the line integral by the two following methods.

(a) directly

(b) using Green’s Theorem

15.–/0 pointsSEssCalcET2 13.4.007.MI.

Use Green’s Theorem to evaluate the line integral along the given positively oriented curve.

C is the boundary of the region enclosed by the parabolas

16.–/0 pointsSEssCalcET2 13.5.001.

Consider the given vector field.

(a) Find the curl of the vector field.

curl F =

(b) Find the divergence of the vector field.

div F =

xy dx + x2y3 dy

C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 4)

5y + 3e dx + 10x + 9 cos y2 dy

C x

y = x2 and x = y2

F(x, y, z) = (x + yz)i + (y + xz)j + (z + xy)k

17.–/0 pointsSEssCalcET2 13.5.007.

Consider the vector field.

(a) Find the curl of the vector field.

curl F =

(b) Find the divergence of the vector field.

div F =

18.–/0 pointsSEssCalcET2 13.5.013.

Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.)

+ K

19.–/0 pointsSEssCalcET2 13.5.511.XP.

Determine whether or not the vector field is conservative. If it is, find a function f such that F = ∇f. If the vector field is not conservative, enter NONE.

+ K

F(x, y, z) = 9ex sin y, 3ey sin z, 8ez sin x

F(x, y, z) = 12xy2z2i + 8x2yz3j + 12x2y2z2k

f(x, y, z) =

F(x, y, z) = y cos xy i + x cos xy j − 2 sin z k

f(x, y, z) =

20.–/0 pointsSEssCalcET2 13.4.019.

Use one of the formulas below to find the area under one arch of the cycloid

x = t − sin t, y = 1 − cos t.

A = x dy = − y dx = x dy − y dx

C

C

1 2

C

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