Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.

Get a Professional Answer

Via email, text message, or notification as you wait on our site. Ask follow up questions if you need to.

100% Satisfaction Guarantee

Rate the answer you receive.

Ask MrBill31 Your Own Question

MrBill31, Engineer

Category: Homework

Satisfied Customers: 85

Experience: BS General Physics and Chemistry MS Physics specialty biophysics

8649121

Type Your Homework Question Here...

MrBill31 is online now

What is the value of the line integral_C F·dr?

Resolved Question:

1- Suppose F = F(x,y, z) is a gradient field with F = Ñf , S is a level surface of f, and C is a curve on S. What is
the value of the line integral_C F·dr?

2- Consider the vector field F(x,y) = (2x2 +y2,2xy). Compute
the line integrals_C1 F· dr and Integral_C2 F· dr, where C1 is the curve

r1(t)=(t, t2) for 0t 1 andC2 is the curve r2(t)=(t, t), also
forR0 <= t <= 1.

Integral_C1 F·dr = .
Integral_C2 F·dr =

Can you decide from your answers alone whether or not F is
a conservative vector field? (Y/N)
Is F a conservative vector field? (Y/N)

3- Let F(x,y) = (-yi+xj)/(x2+y2) = P(x,y)i+Q(x,y)j and let C be the circle r (t) = (cost) i+(sint) j, 0 <= t <= 2p.
A.
dQ/dx=

Note: Your answer should be in terms of x and y; e.g. ”3xy - y”
B.
dP/dy =
Note: Your answer should be in terms of x and y; e.g. ”3xy - y”
C.
Integral_C F·dr =
Note: Your answer should be a number

3- Suppose C is any curve from (0,0,0) to (1,1,1) and
F(x,y, z) = (3z+4y) i+(2z+4x) j+(2y+3x)k. Compute the
line integral_C (F·dr).

4- Let F = (5xy,2y2) be a vector field in the plane, and C the
path y = 5x2 joining (0,0) to (1,5) in the plane.
Evaluate Integral_C (F·ds)

6- Determine whether the given set is open, connected,
and simply connected. For example, if it is open, connected, but
not simply connected, type ”YYN” standing for ”Yes, Yes, No.”
A. {(x,y) |x > 1,y < 2}
B.

(x,y) |2x2+y2 < 1

C.

(x,y) |x2-y2 < 1

D.

(x,y) |x2-y2 > 1

E.

(x,y) |1 < x2+y2 < 4

I really need it tonight my homework is due tonight. ASAP

1- Suppose F = F(x,y, z) is a gradient field with F = Ñf , S is a level surface of f, and C is a curve on S. What is the value of the line integral_C F·dr?

Zero.

If you follow a level surface, the gradient and hence F is everywhere perpendicular to the curve

F*dr = 0 so the integral must be zero

2- Consider the vector field F(x,y) = (2x2 +y2,2xy). Compute the line integrals_C1 F· dr and Integral_C2 F· dr, where C1 is the curve

r1(t)=(t, t2) for 0t 1 andC2 is the curve r2(t)=(t, t), also forR0 <= t <= 1.

Integral_C1 F·dr = .

Int[(i(2x^{2}+y^{2})+j(2xy))*(idx + jdy)]

= Int[(2x^{2}+y^{2})dx +(2xy)dy)]

Here x=t,

y=t^{2}

dx = dt

dy = 2tdt

Integral_C1 F·dr = Int(t=0 to 1)[(2t^{2}+(t ^{2})^{2})dt +(2tt^{2})2tdt)]

Integral_C1 F·dr = Int(t=0 to 1)[(2t^{2}+ t^{2})dt +(2tt)dt)]

= Int(t=0 to 1)[(5t^{2}dt]

= ((5/3)t^{3})(t=1 - t=0)

= 5/3

Same value

Can you decide from your answers alone whether or not F is a conservative vector field? (Y/N)

OHHHH! Nasty trick question!

The answer is NO

Yes these 2 independent paths give you the same result, but NO this is not sufficient to prove F is a conservative vector field (i.e. it is path independent).

It might be sheer coincidence that these 2 paths gave the same result.

A true proof that the path integral is completely independent for all possible paths (conservative) is to show that the gradient field can be written as the gradient of some scalar field.

Is F a conservative vector field? (Y/N)

Answer YES

Let's find out.

Can I write this field as the gradient of some function?

dF/dx = 2x^{2}+y^{2 }

implies F = (2/3)x^{3 }+ y^{2}x

dF/dy = 2xy

so this works

The fact that the field is a gradient of a function

(in this case F(x,y) = (2/3)x^{3 }+ y^{2}x)

means the answer is YES

(and also proves path independence for any path integral).

3- Let F(x,y) = (-yi+xj)/(x2+y2) = P(x,y)i+Q(x,y)j and let C be the circle r (t) = (cost) i+(sint) j, 0 <= t <= 2p.

Ah hah! so this is the problem I have been having with some of your homework problems

"p" as in 0 <= t <= 2p means pi i.e 3.1415 etc,

didn't know this until now.

A. Note: Your answer should be in terms of x and y; e.g. "3xy - y"

6- Determine whether the given set is open, connected, and simply connected. For example, if it is open, connected, but not simply connected, type "YYN" standing for "Yes, Yes, No." A. {(x,y) |x > 1,y < 2}

YYY

(open, one region, no holes) B.

(x,y) |2x2+y2 < 1

NYY

(closed: a filled ellipse, one region, no holes)

C.

(x,y) |x2-y2 < 1 YYY

(open: (filled area between 2 hyperbolas, x = +- sqrt(1+Y^{2})), single region, no holes)

I have 2 more questions if you don't mind and need them now. My homework is due in 2:30 min form know. Please help. Thank you

1- Let{F} = (18 xyz + 3sin x, 9 x^2z, 9 x^2y). Find a function f so that {F} = f, and f(0,0,0) = 0.

2-

For each of the following vector fields F , decide
whether it is conservative or not. Type in a potential function f
(that is, Ñf = F). If it is not conservative, type N.
A. F(x,y) = (-12x+2y) i+(2x+2y) j

f (x,y) =

B. F(x,y) = -6yi-5xj

f (x,y) =

C. F(x,y, z) = -6xi-5yj+k

f (x,y, z) =

D. F(x,y) = (-6sin y) i+(4y-6x cos y) j

f (x,y) =

E. F(x,y, z) = -6x2i+2y2j+1z2k

f (x,y, z) =

Note: Your answers should be either expressions of x, y and z (e.g. “3xy + 2yz”), or the letter “N”

1- Let{F} = (18 xyz + 3sin x, 9 x^2z, 9 x^2y). Find a function f so that {F} = f, and f(0,0,0) = 0.

So I guess you want the potential this is the gradient of:

df/dx = 18 xyz + 3sin x

f = 9x^{2}yz + -3cos(x) + ?

df/dy = 9 x^{2}z

f = 9x^{2}yz + ?

df/dz = 9x^{2}y

f = 9x^{2}yz + ?

So looks like

f = 9x^{2}yz - 3cos(x) + constant

f(0,0,0) = 0 = 0 - 3 + constant

constant = 3

f = 9x^{2}yz - 3cos(x) + 3

2-

For each of the following vector fields F , decide whether it is conservative or not. Type in a potential function f (that is, Ñf = F). If it is not conservative, type N. A. F(x,y) = (-12x+2y) i+(2x+2y) j

df/dx = -12x + 2y

f = -6x^{2} + 2xy + ?

df/dy = 2x + 2y

f = 2xy + y^{2}

f(x,y) = -6x^{2} + 2xy + y^{2}

B. F(x,y) = -6yi-5xj

a rotational flow, suspect not

df/dx = -6y

f = -6xy + ?

df/dy = -5x

f = -5xy + ?

These are the same term with different constants.

Integrability conditions cannot be satisfied.

There is no potential function.

f (x,y) = N (i.e. NO)

C. F(x,y, z) = -6xi-5yj+k

df/dx = -6x

f = -3x^{2} + ?

df/dy = -5y

f = -(5/2)y^{2} + ?

df/dz = 1

f = z + ?

f (x,y, z) = -3x^{2} + (5/2)y^{2} + z

D. F(x,y) = (-6sin y) i+(4y-6x cos y) j

df/dx = -6sin(y)

f = -6xsin(y) + ?

df/dy = 4y-6x cos y

f = 2y^{2} -6xsin(y) + ?

f (x,y) = 2y^{2} -6xsin(y)

E. F(x,y, z) = -6x2i+2y2j+1z2k

df/dx = -6x^{2}

f = -2x^{3} + ?

df/dy = 2y^{2}

f = (2/3)y^{3} + ?

df/dz = z^{2}

f = (1/3)z^{3} + ?

f (x,y, z) = -2x^{3} + (2/3)y^{3} + (1/3)z^{3}

Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N".

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.

JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.

Web sites like justanswer.com/legal ...leave nothing to chance.

Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.

Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.

I will tell you that...the things you have to go through to be an Expert are quite rigorous.

What Customers are Saying:

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C.Freshfield, Liverpool, UK

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C.Freshfield, Liverpool, UK

This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!AlexLos Angeles, CA

Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.GPHesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.JustinKernersville, NC

Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. EstherWoodstock, NY

Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. RobinElkton, Maryland

He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.DianeDallas, TX

Meet The Experts:

LogicPro

Engineer

Satisfied Customers:

4925

Expert in Java C++ C C# VB Javascript Design SQL HTML