What is Arc length: Definition and 286 Discussions

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...

Homework Statement Suppose you are headed toward a plateau 60 m high. If the angle of elevation to the top of the plateau is 25*, how far away from the plateau are you in meters? Homework Equations S = (theta)r The Attempt at a Solution In my head this translates as I am given...

Homework Statement Homework Equations l = int( sqrt( 1 + (dy/dx)^2) dx) from a to b The Attempt at a Solution So far I'm stuck at the R^2 thing. I know if it was just R it would mean the set of all real numbers, but I'm not sure as to what R^2 means and I don't know how to google...

Homework Statement find arc length of curve over the interval t(0,2pi) r(t) = 10cos3t i + 10sin3t j The Attempt at a Solution i apply the formula integral ||r'(t)|| over the interval 0,2pi i get integrate sqrt((-30cos2tsint)2 + (30sin2tcost)2) and then finally get 15sin2t |0 to 2pi and i...

Homework Statement Today we went over finding the arc length s of a circle with a given radian and radius... Thus s = radian*radius... Thats easy to remember but I think it will be more memorable for the long run if I knew the proof and understood it... can some one please post a website...

Homework Statement r(t)=cos(t^2)\hat{i}+sin(t^2)\hat{j}+t^2\hat{k} Compute the arc length integral from t=0 to t=\sqrt{2 \pi}Homework Equations Arclength = \int_{a}^{b}||v(t)||\, dtThe Attempt at a Solution I did the following: \\r'(t)=-2tsin(t^2)\hat{i}+2tcos(t^2)\hat{j}+2t\hat{k}\\...

I always read in applications of integration is to figure out the arc length but they never tell us what is it good for I also couldn't find immediate results by using google, so can anyone tell me its uses?

Hello there, suppose i want to find the arc length of a circle x^2+y^2=R^2 using integration, implicitly differentiating the equation, i find y'=-(x/y) now, arc length (circumference)= (\int \sqrt{1+y'^2}dx putting the value of y'=-(x/y) and substituting for y^2 from the equation of the...

Homework Statement This is another problem my teacher game me. Given the Polar function r=6*sin(t/2) where the variable t is the angle theta in radians, and that t is between 0 and 2*Pi inclusive. Find the distance around the perimeter of the graph. Hint: this is arc length , round to the...

Homework Statement I appologize if this is in the wrong topic. But, I need help with the. I know you guys don't exactly give out the answer, but I'm looking for a particular rule of something that will help me. My calculus professor told me to use any available resource to solve this problem...

Homework Statement F(x) = (4/5)*x^(5/4) on the interval of [0,4] Find the Arc Length Homework Equations Arc Length = Integral (sqrt (1 + [f(x)']^2)) dx The Attempt at a Solution F'(x) = x^(1/4) Integral from [0,4] of Sqrt (1 + x^(1/2)) dx I'm not sure where to go with this...

NVM bout the arc length, need help on integrations Homework Statement Integrate sqrt(1+3x)Homework Equations Sqrt (1+3x) The Attempt at a Solution i made it into (1+3x)^(1/2)

This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...

Homework Statement Find the arclength of the section y=x2 between points (-2,2) and (2,4) Homework Equations L = \int\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}The Attempt at a Solution So what I did first is find the derivative of y=x2 which is y'=2x So I put that into the formula and get...

Homework Statement Given y = 156 - (x - 40)2/60. x = 0 and x = 85 Find distance traveled Homework Equations Arc Length S = integral of square root of ( y' )2 The Attempt at a Solution Doing this I get the trig sub tan(t) = (x - 40)/ 30 (Told by teacher to use this instead of...

Sorry, latex is being weird. I'm currently trying to come up with a way to find an equation that satisfies: s=\int_a^b \sqrt{(f'[x])^2+1} \, dx Which is arc length and G=\int_a^b f[x] \, dx which is area under the curve where A and s are known values, and f[a]=A, f[b]=B...

Getting the "Arc Length Function" Homework Statement I have two problems scanned, one is an in class example and one is from the homework. The book uses the standard arc length of a curve equation to get the answers. Later in the same chapter they introduce the Arc Length Function, using 's'...

Homework Statement Find the arclength of the curve r(t)=(10t^2,2*sqrt(10)*t, ln t) for 1<=t<=8 Homework Equations The Attempt at a Solution i took the derivative of each component of vector r 20t,2sqrt(10),1/t then i square each term and square root it int sqrt( 400t + 40 +...

(Note: cross posted to http://www.devmaster.net/forums/showthread.php?t=16227 ) Hey everyone, As we know, the arc length of a cubic Bezier spline is kinda hard to calculate. There's no closed-form mathematical expression, so most people just subdivide it into a bunch of line segments and...

Homework Statement Maybe this is precalculus? Either way, here is a question that I am curious about. Take a circle of radius R and sweep out an arc length SAB with endpoints 'A' and 'B' over angle theta. For a short enough arc length, I believe that we could approximate SAB by the chord...

I need to find the arc length of the function f(x) = 4/5*X5/4 from [0,4]. You have to find f '(x) first and that would be X1/4 I square f '(x) and obtain X1/2 or \sqrt{X} I plug it into the formula and get S = \int\sqrt{1+\sqrt{X}} from [0,4] I don't know how to evaluate the...

Homework Statement Find an arc length parametrization of the curve r(t) = <e^t(cos t), -e^t(sin t)>, 0 =< t =< pi/2, which has the same orientation and has r(0) as a reference point. Homework Equations s = int[0,t] (||r'(t)||) The Attempt at a Solution So I found the derivative of r(t), and...

Homework Statement Find the length of the cardioid with equation r = 1 + cos (theta) located in the first quadrant Homework Equations f (theta) = 1 + cos (theta) f'(theta) = -sin (theta) s = antiderivative (0 to (pi/2)) sq rt (f(theta)^(2) + f'(theta)^(2)) d(theta) The Attempt at...

Homework Statement Find the length of r = theta^(2) for 0<=theta<=pi Homework Equations Arc length s = antiderivative of sq rt (f (theta)^(2) + f (derivative theta)^(2)) The Attempt at a Solution I have worked my way to the antiderivative of sq rt (theta^(4) + 4(theta)^(2)) but I'm...

In the polar formula for arc length, ds^{2}=dr^{2}+r^{2}d{\theta}^{2}, what is the exact meaning of the r^2 term multiplying d{\theta}^2? Is it an initial distance from the origin? A final distance from the origin? The change in r from point a to point b? This baffles me to no end and nothing...

Homework Statement 1. Find the length of the curve from t=0 to t=1. r(t) = <2t, t^2, (1/3)t^3> 2. 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)cos2t, 2, e^(2t)sin2t>Homework Equations S = \int{r'(t)} dt...

What does the arc length parametrization mean?

Homework Statement find the arc length of f(x) (x^(5/4))/5. The integration limits are from 0 to 4. Homework Equations The arc length formula is integrate sqrt(1 + (f'(x))^2) The Attempt at a Solution f'(x) = (5/4)*(1/5)*x^(1/4) = x^(1/4)/4 integral of sqrt(1 +...

Homework Statement Consider the graph (see attachment) of r = 1 +2cos\Theta in polar coordinates. SET UP integrals to find 1. the area inside the large loop minus the area of the small loop. 2. the arc length of the small loop 3. the surface area of the surface formed by...

Homework Statement For the curve y=\sqrt{x} , between x = 0and x = 2, find (a) the area under the curve, (b) the arc length, (c) the volume of the solid generated when the area is revolved about the x axis, (d) the curved area of this solid. Homework Equations ds = \sqrt {1+(y')^{2}}dx...

Hi, I've been having some issues in solving this problem. Homework Statement Find the arc length of r=2/(1-cosθ) from π/2 to πHomework Equations L =(integrate) sqrt(r2+(dr/dθ)2)dθ The Attempt at a Solution I found (dr/dθ) = (-2sinθ)/(1-cosθ)2 so (dr/dθ)2 = (4sin2θ)/(1-cosθ)4 Then r2 =...

I am having trouble doing exactly what the title says. I have two points and the arc length between them (this is a bending beam type of a situation). Essentially I know where the ends of the beam are and how long the bent beam is and I need to get the equation of the circle. And yes I...

Homework Statement Find the arc length of the projectile from launch until the time it hits the ground, given that 0 V is 100 feet/sec and is 45 degrees. Homework Equations Arc Length= ∫_a^b▒√(█(1+(f^' (x) )^2@)) dx Arc Length of Curve= ∫_a^b▒〖v(t)dt=∫_a^b▒√((dx/dt)^2+(dy/dt) )〗^2...

Homework Statement The task is to solve for the arc length of an ellipse numerically. a & b are given for an ellipse centered at the origin and a value for x is given. Homework Equations Equation of ellipse is given to be x^{2}/a^{2} + y^{2}/b^{2} = 1 and the equation to solve for the arc...

Homework Statement http://i47.tinypic.com/1z6naa.jpg Note... I used wolfram alpha to get the answer, I did not get it myself... So I still need help. The answer shown is correct, so you'll know if you got it. Homework Equations Integral [0, ln(4)] sqrt(1+(dy/dx)^2) The Attempt at a...

Homework Statement Find the arc length of the curve: y=\frac{x^5}{6}+\frac{1}{10x^3} 1\leqx\leq2 Homework Equations ds=\sqrt{dx^2+dy^2} ds=\sqrt{1+\frac{dy}{dx}^2}dx The Attempt at a Solution \frac{dy}{dx}=\frac{5}{6}x^4-\frac{3}{10x^4}...

Find the exact length of the curve analytically by antidifferentiation: y = (x3/3) + x2 + x + (1/(4x +4)) on the interval 0 < x < 2So I set it up using the length of a curve formula: L = \int\sqrt{1+(x^2+2x+1+(\frac{-1}{4(x+1)^2}} And simplified it to L =...

Arc length of y=ln((e^(x)+1)/(e^(x)-1)) on [a,b] Using L=\int\sqrt{1+(y')^2}dx on [a,b] I am having difficulties differentiating y and plugging the results back into get a useful integral. So far I have y'=2e^(x)/(e^(2x)-1)

Hey guys, I'm studying for a test in calc 3 tomorrow and have run into a problem. On the practice test we have a problem "Find the length of the curve: r=theta^2, 0≤theta≤pi/2" I know the length of a curve in polar coordinates is int(sqrt(r^2 + (dr/dtheta)^2))dtheta...but when I get to where...

In a line integral with respect to arc length, we have something like f(x, y)ds "inside" the integral sign. The ds tells us that we are working with the arc length function s, taking diferences (s_K+1 - s_k) in the sums that tend to the line integral. Question: do we shall understand that...

If we have a fly in a room, its position respect to some frame of reference will change with time, so if we want to describe the fly's movement with a parametrized curve, it is easy to see the convenience of taking time as the parameter. I read that we can also take the length of the curve as...

Why is arc length of a function f(x) from a to b defined as \int_a^b \sqrt{1+(f'(x))^2} dx? Where they get the idea of squaring the derivative, adding 1, taking the square root, and then integrating it is beyond me.

a derivation of the formula for arc length is simple enough: given a function f[x], find the length of the arc from x0 to x1. lim(x1-x0)/n=dx n->inf x1 S=^{i=n-1}_{i=0}\sum\sqrt{(x+(i+1)dx-(x+idx))^2+f(x+(i+1)dx)-f(x+dx))^2} xo...

In calculus, the definition of the arc length of some curve C is the limit of the sum of the lengths of finitely many line segments which approximate C. This is a perfectly valid approach to calculating arc length and obviously it will allow you calculate correctly the length of any...

? i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical. also, if it matters, the curve is assumed to be closed.

Homework Statement Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case. r(t) = (c2/a)cos3t i + (c2/b)sin3t j where i and j are the usual unit vectors, 0 \leq t \leq 2\pi, c2 = a2 - b2, and 0...

Hey guys, Got a bit of a problem with a question I found in a textbook. I can do most of it but there's one little part I'm really struggling with: A curve C is given parametrically by: x=t-tanht, y=secht, t\geq0 The length of arc C measured from the point (0,1) to a general point...

Homework Statement Find the arc length of r(t)= <10sqrt(2), e^10t, e^-10t>, 0 <_ t <_ 1. <_ is greater than or equal to. Homework Equations arc length= integral(magnitude of the derivative of r(t)) The Attempt at a Solution i thought I figured the answer out and got an arc...

Homework Statement Find Arc Length: r(t)=t^3 i+tj+(1/2)\sqrt{6}t^2k 1\leqt\leq3Homework Equations The arc length formula: integrate: sqrt((dx/dt)^2+(dy/dt)^2+(dz/dt)^2) dtThe Attempt at a Solution I can find the derivative and plug into the formula, it's just the simplification that is...