Arc length Definition and 281 Threads

Homework Statement the graph of the equation x^(2/3) + y^(2/3) = 7^(2/3) is one of the family of curves called asteroids. Homework Equations find the length of first-quadrant and multiply by 8. 1. y=(7^(2/3) - x^(2/3))^(3/2)) ; 7sqrt(2)/4 <= x <= 7 The Attempt at a Solution...

Good morning, I'm trying to compute the arclength (geodesic distance) between two n-dimensional points over a n-dimensional sphere (hypersphere). Do you know if it is possible? If yes, please, I'd be very pleased if you, as experts, provide me this knowledge. Thank you very much

I don't understand why finding the arc length is always difficult. I understand the formula and know pretty much all the integration methods, but whenever I try to find the arc length of a function like 8x2 = 27y3 from 1 to 8 it's unusually difficult. I would start by solving for x...

x = t + cot t y = t - sin t 0 ≤ t ≤ 2π Somehow the answer is: 2π ∫sqrt(3 - 2*sin t - 2*cos t) dt 0 I'm afraid I don't know where to start on this one. I don't need someone to walk me through it (probably) but a point in the right direction would be appreciated.

Hello everyone, I am having a bit of an issue evaluating the arc length of the function 1/2(e^x+e^-x) interval [0,2]. We were instructed to solve using the arc length formula square root of 1+(dy/dx)^2. The solution should be 3.627 according to my CAS. However my calculations are yielding 3.511...

Yesterday on another forum, someone asked for the launch angle which will maximize the arc-length of the trajectory for a projectile, assuming gravity is the only force on the projectile after the launch. I eliminated the parameter t to get the trajectory: $\displaystyle...

1. v=s/t where s represents the displacement 2. s=rθ where s represents the arc length v=rθ /t Why can substitute here? I guess that is not same things. An arc length is not a straight line but displacement is which is shortest distance between initial and final point.

Hi folks. I'm working on an arc length problem, and my answer doesn't match the answer that our professor gave, so I was hoping that someone could point out where I'm going wrong here. Homework Statement Find the arc length determined by x^2=y^3 from (0,0) to (1,1).all of the work is in the...

Homework Statement Find an arc length parametrization of the circle in the plane z=5 with radius 6 and center (4,1,5) Homework Equations ||r'(t)||=r'(u) s=integral r'(u)du The Attempt at a Solution I get the equation of the circle to be (x-4)^2+(y-1)^2+(z-5)^2=6^2 Not sure where...

If we divide the polar curve into infinitely thin sectors, the arc length of a single sector can be approximated by ds = \frac{dθ}{2π}2πr = rdθ. So why can't we model the arc length of the curve as \int^{β}_{α} rdθ It turns out that the correct formula is actually...

I don't understand the intuition/proof of why arc length = arc angle * radius. This may be partially because I don't fully understand the concept of radians, but anyhow please help.

I have a parabola centered at x=0, equation: y = a*x^2 + c, where a is always negative and c always positive. I need to find a way to calculate a and c, if i know: the arc length above the x axis, and the base width, knowing the base width i also know the x-axis intersections x1,2 =...

Homework Statement 27. Use the parametrization x = tcost, y = tsint of the Archimedean spiral to find the arc length of the first full turn of this spiral (corresponding to 0 <= t <= 2∏ ). Homework Equations The Attempt at a Solution I use onenote and a tablet, so my exact attempt in in the...

Homework Statement r(t)=ti+2tj+(t^2-3)k or r(t)=(t, 2t, t^2-3) 0≤t≤2 Homework Equations arc length formula ∫[the scalar of dr/dt] I know I can calculate the arc length through the equation above, but the questions asks for me to utilize this formula. ∫√(t^2+a^2) dt =...

Homework Statement So, the question gives a particle traveling over a path \gamma, and I need the arc length. Homework Equations The path is \gamma(t) : [1,4] \to ℝ^3, t \mapsto (t^2/2, t, ln(2t)). We want the arc length over 1 \le t \le 4. The Attempt at a Solution First, the...

Homework Statement I was wondering if I did this problem correctly as I don't have the solution, also wanted to make sure that my limits of integration were correct as they tend to be tricky in finding arc length in polar coordinates. x(t)=arcsint y(t)=ln(sqrt(1-t^2)) Homework...

Homework Statement Find arc length of the graph of r(t) = ti + ( (t6/6) - (6/t4) )j + t√3 k 1≤t≤2 Homework Equations Arc length = ∫ ||dr/dt|| dt (Integral from t0 to t1 of norm of derivative of r) The Attempt at a Solution dr/dt = i + (t5 + 24/(t3) )j + √3 k 12 = 1 (√3)2 = 3 (t5 + 24/(t3)...

I am reading Thurston's book on the Geometry and Topology of 3-manifolds, and he describes the metric in the Poincare disk model of hyperbolic space as follows: ... the following formula for the hyperbolic metric ds^2 as a function of the Euclidean metric x^2: ds^2 = \frac{4}{(1-r^2)^2} dx^2...

Hi everyone! I have two questions, one about area of surface of revolution and another is about arc length... I really fail to do this two question despite many times of trying so I hope someone can help me 1. Find the area of the surface of revolution generated by revolving the arc of the...

If the circumference of the region bounded by the curve y=cosh(x) and the lines y=0 x=a and x=-a is 2a+4, where a>0 find the area of the surface obtained by rotating the part of the curve y=cosh(x) between x=a x=-a and around the x axis. This is my homework question.I tried to solve it.I...

Hi everyone ... I am a first time poster from South Africa. I have been visiting the forum for some time. I am busy teaching myself calculus and physics. I have hiccup with the concept of definite integral and arc length of a function. In my understanding these should be the same thing...

Homework Statement Find the arc length of the ellipse or deformed circle. r^2=x^2+(y/β)^2 r=radius β=dilation constant k="random" constant Homework Equations The Attempt at a Solution I suspect it's impossible but I can't prove that. After working it out I got stuck with these...

∫Homework Statement Use the integration tables to find the exact arc length of the curve f(x)=ln x 1≤x≤e Reference the table number formula used Then approx. your answer and compare that to the approx. "straight line distance" between 2 points coordinates of two points...

Homework Statement Let c(t) be a path and T the unit tangent vector. What is \int_c \mathbf{T} \cdot d\mathbf{s} Homework Equations The unit tangent vector of c(t) is c'(t) over the magnitude of c'(t) : \mathbf{T} = \frac{c'(t)}{||c'(t)||} The length of c(t) can be represented by ...

Homework Statement Find the length of the polar curve. Complete the cardioid r=1+cosθHomework Equations L=∫αβ√[f(θ)2+f'(θ)2] dθ The Attempt at a Solution Given f(θ)2 is equal to cos2θ+2cosθ+1 and f'(θ)2=sin2θ I arrive at the integral ∫αβ√[2cosθ+2] dθ which I cannot for the life of me...

Reparametrize the curve R(t) in terms of arc length measured from the point where t = 0 R(t) is defined by x = et, y = \sqrt{2}t, z = -e-t Arc length S = ∫ ||R'(t)||dt ||R'(t)||= sqrt{\dot{x}2 + \dot{y}2 + \dot{z}2}The attempt at a solution Getting R'(t) ==> x = et, y = \sqrt{2}, z = e-t...

->ds/dt where s is the arc length in cartesian coordinates is ((dx/dt)^2+(dy/dt)^2)^(1/2). -> Therefore by the chain rule ds/dt = ds/dp * dp/dt, but if I substitute dx/dt=dx/dp* dp/dt and dy/dt= dy/dp* dp/dt in the formula above, I get ds/dt=ds/dp * |dp/dt|?? What is happening? ->Even by...

How can I find the radius of a circle by knowing two points and its arc length? Do I have to use a numerical method to solve for a trigonometric equation or is there any algebraic or geometric method?

Homework Statement This is probably very simple, but I'm teaching myself arc length via Paul's Online Calculus Notes and there's a simplification on the page: I was wondering why the first Δx^2 was simplified to 1? I understand the other Δx^2 came out of the square root.

http://www.up98.org/upload/server1/01/z/cllb59cvnwaigmmar6b5.jpeg What is the method of calculating arc length in In the image above . x & y is known Thanks .

Homework Statement Find the arc length of y=x*e^(x^6) where 0 ≤ x ≤ 3 Homework Equations The Attempt at a Solution I took the derivative of the equation and squared it to get (e^2(x^6))(1+12(x^6)+36(x^12)) then plugged it into the proper formula to get: 3...

Homework Statement Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. Homework Equations r(t) = (-3tcost)i + (3tsint)j + (2\sqrt{2})t(3/2)k 0 ≤ t ≤ ∏ The Attempt at a Solution So I found dr/dt (I think), which is v(t) =...

I'm trying to find the equation for a circle given two points in x, y and the starting angle, arc length, and two points along the circle. I need to find the equation because I need to translate a sprite along the curved path from one point to another. The situation ends up looking like this:A...

Homework Statement Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t. r(t) = [e^(2t)cos(2t)]i+2j+[e^(2t)sin(2t)]k Homework Equations i know that the derivative of the arc length with respect to t = magnitude of...

Homework Statement My textbook [Engineering Mathematics, Stroud, 6th Edition, page932] runs through the derivation of the integral formula for arc length. I got confused at one of the steps: [partial](ds/dx)=sqrt(1+([partial](dy/dx))^2) if [partial]dx tends to 0...

I'm just wondering because I'm really confused right now. My teacher gave us the formula: K= \frac{1}{2}sr for area of a given sector where "s" is the arc length and "r" is the given radius. the formula for the arc length is: s=\Theta r Though, I can't seem to understand how he came up...

So sorry if this has been discussed elsewhere before. I know it may be trivial but for some reason I just can't get it. I simply can't seem to integrate the square root of (1 + 1/4x). This problem has been highlighted for a reason, but I'm missing the point. Any input is much appreciated.

There are line integral with respect to arc length and line integral with respect x/y. I know \int_C Pdx+Qdy is useful to calculate the work. When do we need the line integral with respect to arc length?

Homework Statement Determine the arc length of the function on the given interval x = (y^4)/8 + 1/(4y^2) from 1 to 2 The arc length formula \int (f'(x)2 + 1).5 dx The Attempt at a Solution I used the arc length formula but don't know where to go from here. Usually these...

This is an engineering problem that involves geometry so I thought this would be the best forum to post in. I am attempting to interpolate elevations of roadway lines offset from a baseline (center line of a roadway) between two points. The coordinate system used is a combination of stations and...

First of all hello, I am new to this forum and I decided to join in order to exchange some information with other members that are more knowledgeable than me in the area of diff. geometry. My background is computer science but I am not a student. I am only now starting to learn about diff...

Homework Statement Let c be the path c(t)=(2t,t^2,logt), defined for t>0. Find the arc length of c between the points (2,1,0) and (4,4,log2) I just have a problem with the limits for the integral...what limits so I set for it after finding the derivative and using Pythagorean...

Homework Statement Equation of a circle is: x^2+(y+a)^2=R^2 x intercepts are +/-\sqrt{3} and arclength above x-axis is \frac{4\pi}{3} Find a and R.

Homework Statement Find coordinates of a piont on an arc from beginning coordinates at the arc distance of 6.6821. Given Radius of 25 at (100,100), Begining coordinates at (125,100), Ending Coordinates at (115.6994,119.6301), with an overall arc length of 22.4472. Homework Equations...

Homework Statement Confirm that th definition of th arc length ds^{2}=dr.dr leads to the formula L=\int_{C}\frac{dr}{dt}dt Homework Equations \frac{dr}{dt}=\frac{dx}{dt}+\frac{dy}{dt}+\frac{dz}{dt}dt The Attempt at a Solution I am really unsure of what to do here. I have tried starting at...

Homework Statement Find the exact length of the curve x=e^t + e^-t , y=5-2t , 0≤ x≤ 3 Homework Equations ∫ √ ( (dx/dt)² + (dy/dt)² )dt The Attempt at a Solution My attempt at the solution is hopefully in the attachment. I could use Simpson's and get an approximate length but...

Homework Statement Find the length of the curve y=x^3 using P(1,1) as the starting point Homework Equations f(x) = \int_{a}^{x} {\sqrt 1 + {f'(t)}^2} The Attempt at a Solution So far all I've done is found my y' and plugged it in, giving me 1+9t^4 inside the square...

Homework Statement r = e^θ find arc length from (1,0) to origin Homework Equations ∫ab sqrt (r^2 + (dr/dθ)^2) dθ The Attempt at a Solution ∫10 sqrt ((e^θ)^2 + (e^θ)^2) dθ ∫10 sqrt (2(e^θ)^2) dθ ∫10 sqrt (2) (e^θ) dθ sqrt (2) ∫10 (e^θ) dθ need help converting limits in...

Homework Statement find the length of the curve x = 1/3√y(y-3) 1 ≤ y ≤ 9 Homework Equations L = ∫ √(1 + (dx/dy)^2) The Attempt at a Solution x = 1/3√y(y-3) 1 ≤ y ≤ 9 x = 1/3 (y^3/2 - 3y^1/2) dx/dy = 1/2(y^1/2) - 1/2(y^-1/2) dx/dy = 1/2(y^1/2 -...

Find the arc length of [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP595419ebfac4cg3g1925000036iede4e50653655?MSPStoreType=image/gif&s=4&w=65&h=36 from 0 to 8Formula for Arc Length: integral from a to b of sqrt(1+[f(x)]^2) Attempt: f'(x) = 2/3 * 3/2 * x ^(1/2) f'(x) = x^(1/2) integral...