Line integrals Definition and 132 Threads

Homework Statement i) Define a path \gamma whose image is the ellipse \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 traced counterclockwise. ii) Show that \int \frac{1}{z} dz = \int \frac{1}{z} dz for a suitable circle \beta (NOTE: THE FIRST INTEGRAL IS OVER THE ELLIPSE \gamma, THE SECOND ONE IS...

Homework Statement I'm trying to set up a couple integrals. Suppose you have a closed loop and you want to find its area. You don't know what the shape of the loop is. All you know is that the length of the loop is L. The Attempt at a Solution These are my integrals. I just...

*Please don't just read the first post and leave. I'm adding to the thread with each attempt. I'm not asking someone to do it for me!* I guess this is a lousy first post, and I apologize, but I am desperate and would appreciate all the help I can get more than anyone could imagine! This is...

Hello, I am trying to solve for the surface area of a odd surface for a fire relief PSV and needed to do a line integral but I was reading into my calculus book and going back to the definition of arc length I am confused: L = lim_{n\rightarrow\infty}\sum (P_{i-1}*P_{i}) Multiplication should...

Homework Statement find \int 3x^2 dx +2yz dy + y^2 dz between the points A=(0,1,2) and b=(1,-1,7) by finding a suitable f Homework Equations 3. attempt Isnt f just the partial intergral of the above equation? f =x^3 + zy^2 + zy^2 but solution for f is f =x^3 + zy^2why is...

I have a rough idea of what a line integral is, please correct me if I am wrong: If a function y=f(x) is being integrated over a curve c=g(x), what we are doing is picking points off of the curve c, putting them through f(x) and summing the individual values that we get to infinity (or sum of...

Homework Statement http://www.geocities.com/asdfasdf23135/advcal26.JPG Note: path-connected means arcwise-connected C^0 means continuous ⊿f=Laplacian=(f)xx+(f)yy df/dn = grad f ． n 2. Relevant material Green's theorem, line integrals, ... The Attempt at a Solution The only part...

[SOLVED] Evaluating line integrals Homework Statement I am given a line integral: \int (x^2+y^2)^2ds, where C is a circle of radius 3 with centre in (0;0). Evaluate it. The Attempt at a Solution Ok, first I know (x^2+y^2)^2 = 81. So far, so good. Then I know for an object in the xy-plane...

Homework Statement I am having a bit of trouble relating the line integral of a function with respect to arc length with the line integrals with respect to x and y.

I get an answer for this problem, but its 0 and i think that's wrong. if someone could please, help that'd be great. Homework Statement Find the work using the Line Integral Method: W = Integral of ( Vector F * dr) Vector Field: F(x,y) = (xy^2)i + (3yx^2)j C: semi circular...

I don't really understand the classical notation for line integrals, namely why would you want to represent a scalar function f(x,y) as p(x,y)dx + q(x,y)dy. I also don't fully understand the geometrical interpretation of this. Though solving the problems is easy, I don't really understand what...

Hi, I'm greatly puzzled by the physical meaning of line integrals. Based on my understanding, the line inetgral of a scalar function is taking the integral of a function over a curve. What does this exactly mean? I mean the physical meaning? Just find it hard to absorb and apply the rule...

PROBLEM: Show that the integral \int_{C}^{}\frac{dz}{z^{2}} where C is a path beginning at z=-a and ending a z=b, where a > 0 and b >0, is independent of path so long as C doesn't go through the origin. ----------- WHAT I HAVE DONE: I know from a past assignment that \frac{1}{z^{2}} has a...

What does line integral really mean, what is it doing? Say you have a function f(x,y,z) and you integrate it w.r.t. arc length along some curve C. Is this like finding the area under C over f? Like if you are walking along C, and the vertical area covered below you is the integral? It's...

Hi there I got a couple of question regarding the topic above Homework Statement (a) Given the integrals \int \limit_{0}^{i} \frac{dz}{(1-z)^2} \int_{i}^{2i} (cos(z)) dz \int_{0}^{i\pi} e^{z} dz (1)write this as a Line integral on the form \int_{\gamma} f(\gamma(t)) \cdot...

Could someone help me with the following? I am asked to evaluate the line integral of ∫(y + sin x)dx + (z^2+cosy)dy +x^3dz where C is the curve r(t) = <sint, cost, sin2t, 0 ≤t≤2π. Doesn’t this equal to ∫F∙dr where F = <y + sinx, z^2cosy,x^3> and r = <x,y,z>? So wouldn’t ∫F∙dr =...

Hello Im working on some line integral problems at the moment. The first one is really only a check - I think I've worked it out... Compute the line integral of the vector field B(r) = x^2 e(sub 1) + y^2 e(sub 2) along a straight line from the origin to the point e(sub 1) + 2 e(sub 2) + 4...

How do you find the parameters for x,y,z and so forth. The examples in the book always use x=cos t and y=sint, but I know that there are more options. I'm just lost as to how to look at it. For example the line integral xy^4 ds, C is the right half of the circle x^2+y^2=16 I know this...

Hi, I have been trying to understand the meaning of line integrals, as opposed to the good ol' fashioned regular integral. Graphically, an integral like : \int_{a}^{b} f(x) dx = \lim_{\|\triangle\|\rightarrow 0} \sum_{i} f(w _i) \triangle x_i tells me that the area between the x-axis...

what's the difference between \int_{a}^{b} f(r(t)) dt and \int_{a}^{b} F(r(t)) (dr/dt)dt? (where F is a vector function) because when I'm calculating those two types of questions, the first question just uses dt to integrate the line integral but in the 2nd question, i have to...

Calculating line integrals... Ok, the problem is: h(x,y) = 3x (x^2 + y^4)^1/2 i + 6y^3 (x^2 + y^4)^1/2 j; over the arc: y = -(1 - x^2)^1/2 from (-1,0) to (1,0). In my notes, I had written: if h is a gradient, then the INTEGRAL of g*dr over curve C depends only on the endpoints. Also, if...

I'm really having trouble with this, I can't even understand the example in my textbook. The example problem is: Show that ydx + xdy + 4dz is exact and then evaluate it over some limits. I can show that its exact, and once I find the function, I can evaluate it, so I really just need help...

Thanks on the help on the other thread. I, however, have yet another question. In the line integrals, how is it that we're integrating the various components to the limits of the curves, it seems like the curves really don't matter, just their limits. Can someone explain how the curves are...

Say we have a vector, let's use something simple like A = 2xyi + 3yzj Say we want to find the work done on a particle traversing a path, so we just add up the work done on each path. Let the path be: y = x^2 from x = 0 to x = 5 y = 25 from x = 5 to x = 10 now a final path from...

Quick question, what is the approach to this problem? Keep in mind I am supposed to use the Fundamental Theorem of Line Integrals. \int_{C} 2ydx + 2xdy Where C is the line segment from (0,0) to (4,4). Unless I am missing something I need to make that into the form of \vec{F} \cdot...

Greetings All, I need serious help with this problem , well maybe several problems but I'll take it one at a time: Compute the line integral of (4xz + 2y)dx where C is the line segment from (2,1,0) to (4,0,2). Thanks

Ok the question is: \vec F(x,y)=<3xy,8y^2>\,=3xy\,\hat i + 8y^2\,\hat j C: y=8x^2 Where C joins (0,0)\,,\,(1,8) Evaluate \int_{C} \vec F \cdot d\vec r I'm unsure how to evaluate this. I really do not want just an answer, I want to know how to solve it. My first thought was to check...

:confused: I took multivariable calculus a while back. It was all fine until we got to line integrals and surface integrals divergance etc. Then it seemed like I got the rug swept from beneath me. After taking physics 2 a lot of it makes so much more sense now though. I am reading through that...

with out a picture i find this hard to ask, but... i don't really understand what a line intergral represents physically? like is a 2D plane in a 3D space? i don't understand why you take line intergrals in the shape of a square of some function what does that acutally represent, id appreciate...

Hello, I must be having some sort of brain malfunction or something. First here is my question: Evaluate the line integral with respect to arc length The integral sub C of x*e^y ds where C is the arc of the unit circle from (1,0) to (-1,0) traversed counterclockwise. Now if the...

For our homework this week for Pure, one of the questions is to ingration 1/(16 + x^2) with respect to x between the limits 0 and 4. I know the result from the formula wqith arctan in it, but since we've to use substitituion here and not just plonk down the formula, I'm confused as to what to...

I have to corellate the Carnot cycle with line integrals. This makes sense to me as line integrals can be used to find the work done by a vector field on an object traveling along a certain path. The Carnot cycle places a limit on the efficiency of an engine cycle. My question, how could I...