Arc Definition and 485 Threads

If y = \frac{x^{3}}{6} + \frac{1}{2x}\ and \frac{1}{2}\leq x\leq 1 . Find the arc length. So \frac{dy}{dx} = \frac{x^{2}}{2} - \frac{1}{2x^{2}} . So I got \frac{1}{2} \int^{1}_{\frac{1}{2}} \sqrt{2+x^{4} + x^{-4}} dx . How would you evaulate this? Thanks

Okay, so I was given the parametric equations of x = (cos(t))^2 and y = cos(t). So I found dy/dt = -sin(t) and dx/dt = -2sin(t)cos(t). This is where I am getting stuck, so I have the L = integral from 0 to 4pi (sqrt((dx/dt)^2+(dy/dt)^2)) , but I don't know how to simplify this to get the answer...

Hello everyone. I'm a metal worker trying to do the layout for a project using a few nice curves. To do that, I need to get arc length, but I'm having trouble finding it for f(x)=x^3. If anyone can give me a nudge in the right direction for integrating (1+(3x^2)^2)^1/2, it would be greatly...

..Or I think this is considered that... Here's the problem as written then I'll get to it: Find the length of the curve y^2=x^3 from the orign to the point where the tangent makes an angle of 45 degrees with the x-axis. Okay, by me posting this, I don't want anyone (nor am I looking for...

I have a circular arc of wire centered at the point (0,0). It has a radius of r, extends from \theta = -60 to \theta = 60 and also holds a charge q. For the differential electric field I have the following equation: dE = \frac{\lambda ds}{4 \pi \epsilon_0 r^2} Where ds is the length of a...

I'm having trouble with the following: The problem is to find the arc length of the following parametric function: x=(e^-t)(cos t), y=(e^-t)(sin t) from 0 to \pi I found that \frac{\partial y}{\partial t} = e^{-t}(\cos{t}-\sin{t}) , \frac{\partial x}{\partial t} =...

Hey, I need some help with an arc length question. It is: Find the length of the curve: x=3y^(4/3)-(3/32)y^(2/3) from y=125 to y= 216 So i know i need to use Arc Length=sqrt(1+(dx/dy)^2) but i can't seem to get the right answer. I have the derivative as 4y^(1/3)-(1/16)y^(-1/3). Squaring...

i have 2 calculus questions that are due in the next half n hour and i have no idea how to even start them. I hope somoene can help me in time. Question1 Find the volume of the solid obtained if the plane region E bounded by the curve y=x^2 and y=x^3 between x=0 and x=1 is rotated about the...

Hey I got a project assigned for my Calc 3 class, and I was wondering what to do with the following: A hanging cable has the shape y = 1/c cosh(cx + b) + a for some constants a,b,c with c>0. Suppose the ends are at P(0,10) and P2(30,5). If the length of the cable is known to be 100...

A uniformly charged circular arc AB is of radius R covers a quarter of a circle and is located in the second quadrant. The total charge on the arc is Q > 0. This problem has 4 parts, I got the first 2. 1. The direction of the electric field E due to the charge distribution at the origin is in...

\int^{6}_{0} \sqrt{1-n^2x^2}dx=\pi+e I need to solve this for n. I believe there should only be one possible function of the form y=x^n that gives an arclength of \pi+e over the interval x=0 to x=6, and wish to find the value of n that such a function must have. Does anyone know how to do...

Using trapezoids and N=4, find the length of the arc of the curve y=(1/3)x^3 from (0,0) to (1,1/3).

The problem I am working on asks me to find the curve on the surface z=x^(3/2) which minimizes arc length and connects the points (0,0,0) and (1,1,1). Here's what I did: Integral [sqrt(dx^2+dy^2+dz^2)] Integral [dx sqrt (1+(dy/dx)^2 +(dz/dx)^2] Integral [dx sqrt (1 + (dy/dx)^2 + 9x/4)]...

Finding an arc length I am attempting to find the arc length of y = cuberoot[x] between (1,1) and (8,2). I solved the integral from 1 to 2 of sqrt[1+(3y^2)^2]dy. I used a formula from a table of integrals in my text to solve this integral. The solution I get is 68.19. I can see that this...

How do I find out what angle to fire a projectile so that the height it attains is equiv to the length of its arc? Whats a general formula? Assume the projectile is "fired" from ground level. Say, from a pea shooter or a sling shot.

I am having problems to prove this: Show that a graph G remains connected even after deleting an arc (i,j) iff arc (i,j) belongs to some cycle in G. Grapgh G = (N, A), N = set of points of nodes, and A = set of arcs; an arc is an edge from node i to a different node j from N. Any suggestions?

Hello, I was wondering if someone could check and see that i did this problem right. You need to find the arc length of the vector from t=0 to 1: r= <2e^t,e^-t,2t> So first i took the derivative and got velocity. v=<2e^t,-e^-t,2> Next i used the formula for arc length. arc...

This is my last homework problem and I feel that I almost have it solved. The problem is as followed: f(x) = \sqrt{4-x^2} Find the arc length of the given function from x=0 to x=2. I know that I am supposed to use this formula to solve for arclength: \int_{0}^{2} \sqrt{1 +...

Can anyone tell me what the difference is, if any, between inverse _, arc_, co_, and _^-1, when refereing to any of the trigonometric ratios? Also, what would arcco_, and inverse co_ refer to? Thank you.

Yikes, I am really starting to spam this place up! On the subject of curvature, it says that we can reparametrize the cure in terms of arc length instead of time. If we have time,t, and arc length s(t), we can write it as t=t(s). It seems to me that this is NOT true in general, if you...

i am looking into buying either a stick electrode arc welder or a semi-automatic flux spool fed arc welder does anyone have suggestions about using either/or? thanks

The arc length... Hello all, this is my first post. I am a Computer Engineering Student at Florida A&M University taking Calculus 2 over the summer semester. Should finding the arc length be so extensive?? Are their shortcuts that I am missing? If you don't know the formula, the arc...

I want to find two functions f(n,x) and g(n,x) such that f(n,x)sin(g(n,x)) always has a constant arc length over some interval [a,b]. Where n increases the amplitude but decreases the period. Any suggestions?

A perfect hemisphere of frictionless ice has radius R = 8 meters. Sitting on the top of the ice, motionless, is a box of mass m = 10 kg. The box starts to slide to the right, down the sloping surface of the ice. After it has moved by an angle 14 degrees from the top, how much work has...

here is the problem, and I can't seem to get very far, compute the length of r(t) = <3t, 4cost, 4sint> from t=0 to t=1 i know the formula is integral from 0 to 1 of length of r'(t) but I keep coming up with 5, and it doesn't seem right, can someone please confirm or deny this. Thanks

srry to be a bother but can someone help me on how to do this, it explains it in the book but i don't understand. Here it is: arcsin(sin 3(pi)) i would really appreciate ur help, and thxs before hand. :smile:

Dear . . . Physics Forum May I Ask Some Help ? I need a website that makes me learn more about : 1. Arc Welding Machines . 2. Arc Welding Technology . 3. Welding Rodes Specifications . 4. The Calculations That We Need For How Deciding The Welding Rode Diameter Depending On The Working...

Hi there, I was hoping that somebody could help me. I'm stuck again! :cry: a rod with (lambda) coulombs of charge per meter of its length has the shape of a circular arc of radius R. The rod subtends an angle (theta). Shpw that the magnitude of the electric field at the centre of the...

Hello, i am a high school student currently taking ap calculus. i am currently working on a research project on arc length in polar coordinates. through all of my research thus far the one thing that has eluded my grasp so far that is really frustrating is the applications in real life for...

Hello, I am having trouble remembering some of the material required for my current calculus course so I am reviewing some of the previous material that I have forgotten. I am having trouble following the definition of The Arc Length Function as presented in James Stewart's "Calculus...

Find a function F(x) whose arc length L(x) from (1,1/2) to (x,F(x)), x>1 is (1/2)x^2 + (1/4)Ln(x). First some short hand notation. Int[f(x),dx], means the indefinite integral of the function f(x). Int[f(x),dx,a,b], means the definite integral where a is the lower bound and b is the...

Hi, I'm currently doing an research experiment into the behaviour of plasma around magnetic fields. I will be using an arc welding machine for the plasma and an electromagnet. (So I can adjust the field's intensity as an independant variable.) The arc should bend in the presence of a magnetic...

The first general circle formula is, (x-a)^2+(y-b)^2=r^2 Where M(a,b) and r:radius. I understand this well, but when the subject is arcs... (x-a)^2=r^2-(y-b)^2 x_\textrm{1,2} =a (+-) \sqrt{r^2-(y-b)^2} My teacher said that equations for x1 and x2 were half circles at right and...

Calc help please! Plz help me out w/ the problem below. Thanks. Find the length of the specified arc of the given curve: y=1/3sqrt(x)*(3-x), 0<=x <=3 Formular to find arc length is integral from a to b of sqrt(1+f'(x)^2)dx I got to these steps below and not sure exactly wat to do next...

I'm a little confused by the following in my textbook: Arc Length Function of a curve, 's', is defined by: s(t) = [inte]|r'(u)|du = [inte][squ]((dx/du)^2 + (dy/du)^2 + (dz/du)^2)du integrate both sides and you get ds/dt = |r'(t)|. Arc length is independent of the parameterization...