Arc length Definition and 286 Threads

Homework Statement find the arc length x=2e^t, y=e^-t, z=2t Homework Equations The Attempt at a Solution dr/dt=2e^ti-e^-tj+2 ds/dt=sqrt((4e^2t)+(e^-2t)+4)) dt =integral from 0 to 1 sqrt(4e^4t+4e^2t+1)/e^t sorry about the lack of latex, I have no idea how to integrate this function

Homework Statement Given: The diameter of the Earth is 8000 miles If angle ACB has measure 1', then the distance between A and B is a nautical mile. Approximate the number of and (statute) miles in a nautical mile. Homework Equations Arc Length Therom: s=r(theta) The...

Homework Statement Find the length of \ x =t^{3} \ y =t^{2} 0 \leqt\leq 4 Homework Equations I would write the formula for the arc length but I don't know how to make a definite integral. The Attempt at a Solution I have the whole thing set up and I'm ready to integrate but I...

Homework Statement I'm trying to find the arc length of a curve over an interval and I've arrived at \int (y4 +2y2 +1)1/2 dy and now I'm pretty sure i should use a u substitution in order to integrate. I tried using u=y2 so du=2y dy so dy=du/2y Then you have \int (u2+2u+1)1/2 and...

Homework Statement Find the Arc Length Parameter along the curve from the point where t = 0 by evaluating the integral: s = ∫ |v(τ)| dτ from 0 to t Then find the length of the indicated portion of the curve. Homework Equations The vector I am using for this: r(t) = (etcos t)i + (etsin...

Find the arc length. x = sqrt(t) y = 6t - 2 Interval from 0 to 5 inclusive. Whenever I do this, I get a long answer with big numbers in the numerator all divided by 48. Can someone walk me through the steps? THanks.

Hi, Im trying to calculate the arc length of the function f(x)=x\sqrt{x} From x=1 to x=7 But I am getting the wrong answer and I am not sure why. The formula is \int^{7}_{1}\sqrt{f'(x) + 1} The derivative of f(x) =\frac{x}{2\sqrt{x}} + \sqrt{x} Squaring yields ~~\frac{x}{4} + 2x +1 which...

Homework Statement Find the arc length of the curve described by the parametric equations: x=2e^t & y=3e^3t/2 ln3≤t≤2ln3 Homework Equations S = ∫(a->b) √[(dy/dt)^2 + (dx/dt)^2]dt The Attempt at a Solution Differentiated the two parametrics: dy/dt = 2e^t dx/dt = (3/2)*3e^3t/2 =...

The path taken by a ray of light, from an event E1 to event E2, follows a zero arc length curve such that E2 ∫ds = 0 1. E1 Where S is the interval along the null geodesic path between the...

Homework Statement Consider the path f{r}(t) = (8t, 4t^2, 4log(t) ) defined for t > 0. Find the length of the curve between the points (8, 4, 0) and (24, 36, 4log(3)). Homework Equations \int|r' (t)|dt The Attempt at a Solution r(t)=(8t, 4t^2, 4log(t)) r'(t)=(8, 8t, 4/(ln(10)t)) |r'...

Homework Statement Hello, I have an arc length problem that I’m stuck on, and I would really appreciate it if someone could help me out. I understand the arc length formula and everything, it’s evaluating the integral produced by it. The author in the book I got this problem from tells the...

Homework Statement Find the length of the curve y=x^2-4|x|-x from x=-4 to x=4. The Attempt at a Solution I realized there is a corner at x=0 so i tried to get around this by pluggin in x for x>=0 and -x for x<0. However, my integrals don't match the answer...

Homework Statement I'm trying to compute the circumference of a wing section. I have broken up the airfoil circumference into arc pieces and used cubic splines to come up with an equation for each piece. For example, the arc nearest the leading edge of the wing is the function: y =...

Homework Statement A hawk flying at 2 m/s at an altitude of 80 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation below until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters...

When I take the line integral around a square shape path "C" as follows: From A to B to C to D to A C1 = A(0, 0) to B (4, 0) t i 0 <= t <= 4 C2 = B (4, 0) to C (4, 7) 4 i + (t - 4) j 4 <= t <= 11 C3 = C (4, 7) to D (0, 7) (15 - t) i + 7 j 11 <= t <= 15 C4 = D (0, 7)...

C: y=f(x)=e^x, where x is all real numbers. Compute the arc-length function S for C relative to C's y-intercept Computer the area S for the surface generated by revolving the curve C*:y=f(x)=e&x, where x is [0,a] and a is a positive constant, about the x-axis I've been trying this problem for 2...

Homework Statement ok, the original prob is : find the length of the curve of y=ln(1-x^2) x between 0, 1/2. Homework Equations The Attempt at a Solution ive made it this far: my integral is -1 + 2/1-x^2.....ok so i decompose the second part but in doing so i get a...

Homework Statement Evaluate the line integral \[ \int_c yz\,ds.\] where C is a parabola with z=y^2 , x=1 for 0<=y<=2Homework Equations A hint was given by the teacher to substitute p=t^2 , dp=(2t)dt and use integration by parts. I also know from other line integrals with respect to arc length...

Homework Statement x = 1+3t^2 y=3+2t^3 0<= x <=4 Homework Equations L = integral from a to b of \sqrt{[dx/dt]^2 + [dy/dt]^2} dx The Attempt at a Solution dx/dt = 6t dy/dt = 6t^2 L = integral from 0 to 4 of \sqrt{(6t)^2 +(6t^2)^2} dx = " \sqrt{36t^2 +36t^4} dx = "...

Homework Statement Show that d^2 R / dt^2 is NOT a scalar which is a multiple of d^2 R / ds^2 where R is a vector, s is arc length Homework Equations and The Attempt at a Solution I was thinking maybe it has something to do with the fact k = |d^2 R / ds^2| a = d^2 R / dt^2 = d|v|/dt * T + k...

Homework Statement Find the arclength of the function y=x^2 when x is between 0 and 10. Homework Equations Arclength here is \int_{0}^{10} \sqrt{1+(2x)^2} dx (It's intended to be the integral from 0 to 10 of the quare root of 1+(2x)^2. My latex skills suck.) The Attempt at a...

HELP

Homework Statement Find the arc length of the equation y^2=4(x+4)^3 from x=0 to x=2 Homework Equations L=\int_{a}^{b}\sqrt{1+f'(x)}dx The Attempt at a Solution L=\int_{0}^{2}\sqrt{1+9(x+4)}dx which simplifies in to L=\int_{0}^{2}\sqrt{9x+37}dx and I'm stuck there--how should i try...

Homework Statement Here is difficult one guys, Lets imagine that an object movement along a curve is described by the parameterized function called \omega: I \rightarrow \mathbb{R}^3 which moves on the interval [a,b]\subset I. and this depended on motor which supplies the constant...

Homework Statement Find the arc length oh the graph f(x)=cosx on the integral [0,\frac{\pi}{2}] Homework Equations \int^{b}_{a}\sqrt{1+{f'(x)}^{2}}dx The Attempt at a Solution Alright so I took the derivative of f(x) to get f'(x)=-sinx then I squared it to get sin^{2}x so I could...

How in gods name do I do that? I attempted that integral and... it just can't be integrated! What I tried: That doesn't help one bit... How do I do this? NOTE: No graphing calculator is to be used.

Homework Statement Find the arc length of y=\sqrt{x} from x=0 to x=2. The Attempt at a Solution I don't know, this is a nastier integral than it looks. From the substitutions, s = \int_0^2 \sqrt{1 + \frac{1}{4x}} dx. From doing this over and over again I already know the answer will have...

I know this is very simple, but the end integral just kills me Homework Statement Given equation in Parametric form x=\sqrt{2t+1}), y=6t Find arc length Homework Equations The Attempt at a Solution take x' & y' then Take integral of \int\sqrt{1/(2t+1) + 36} This is where I got stuck ...is...

Homework Statement y = (2/3) * (x^2 - 1) ^ (3/2) 1 <= x <= 3 Length = ?Homework Equations L = \int\sqrt{1 + (dy/dx)^2} dxThe Attempt at a Solution dy/dx y = (2/3) * (x^2 - 1) ^ (3/2) = 2x * sqrt(x - 1) Any ideas for a proper substitution? The answer on wolfram seems ridiculous. :bugeye:

a curve is given as 3 parameters of t: x=a(3t - t^3), y=3a(t^2), z=a(3t + t^3) i have to find the arc length measured from origin and curvature as functions of t. would i be correct in using the integral at the bottom of page 2 here: http://homepages.ius.edu/wclang/m311/fall2005/notes17.2.pdf

Homework Statement Find The length of r=sin³(x/3) 0<x<3pi/2 2. The attempt at a solution well first i found r'=3.cos(x/3).1/3.sin²(x/3)=cos(x/3)sin²(x/3) r²=cos²(x/3)sin^4(x/3) then i put the formula integral of radical (r'²+r²)dx and I'm stuck here any help?

Homework Statement What is the arc length of f(x) = (4-x^2)^(1/2)? Homework Equations The Attempt at a Solution

Homework Statement x = \frac{u^{2} + v^{2}}{2} y = uv z = z Find the arc length given: u(t) = cos(t), v(t) = sin(t), z = \frac{2t^{\frac{3}{2}}}{3} Homework Equations ds^{2} = dx^{2} + dy^{2} + dz^{2} In curvilinear coordinates thhis becomes ds =...

Homework Statement Find the arc length of r(t) = cos(t)^3 i + sin(t)^3 j from t = 0 to t = 2 * Pi It's a hypocycloid that's four cusped. Homework Equations s = \int\sqrt{x'^2 + y'^2} The Attempt at a Solution x = cos(t)^3 y = sin(t)^3 x' = -3cos(t)^2*sin(t) y' =...

Homework Statement find arc length of the segment of the 2space curbe that is defined by the parametric equations x(t) = t-sin(t) y(t) = 1+cos(t) 0 ≤ t ≤ 4π The Attempt at a Solution I've found dx/dt and dy/dt respectively and put them into the arc length equation, i.e...

I am trying to figure out the following arc length problem, and it's really coming down to a question over intregration. Compute the length of the curve r(t)=(4t)i +(4t)j+(t^2+6k) over the interval 0 to 6. I have dr/dt = (4, 4, 2t) , and then used the arc length equation: L= integral...

hi! i need some help here, do you have any available example on how to find the arc length in polar form θ = f (r)? using integral calculus, i mean. i searched the internet but i only got the r= f(θ) example. i hope you can help me. thanks!:)

Two cities on the surface of the Earth are represented by position vectors that connect the location of each city to the centre of the earth. Assuming that the centre of the Earth is assigned the coordinates of the origin, and that the Earth is a perfect sphere, outline the steps that would lead...

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...

How do I solve this ?

I have a question on the formulas for arc length and surface area. Do you use the formula: s= \int_{c}^{d}\sqrt{1+[g'(y)]^2}dy only when you are provided with a function x=g(y)?? Can you convert that to y=g(x) and solve it by replacing g'(y) with y(x), changing the bounds and the dy to dx...

Curves are functions from an interval of the real numbers to a differentiable manifold. Given a metric on the manifold, arc length is a property of the image of the curves, not of the curves itself. In other word, it is independent of the parametrization of the curve. In the case of the...

Doran/Lasenby define a proper interval as: \delta \tau = \int \sqrt{\frac{dx}{d\lambda} \cdot \frac{dx}{d\lambda}} d\lambda (c=1, x= (t,x1,x2,x3) is a spacetime event, and the dot product has a +,-,-,- signature) and say that this is called the proper time. I can see that this...

Homework Statement Length of curve: y=1/2(ex-e-x) from 0 to 2 Homework Equations s = ∫√[1+(dy/dx)^2] dx The Attempt at a Solution [sqrt(4+2e^(-x)+e^x)]*[-1+e^x]/[1+e^x]. = 3.323971

Simplifying an arc length problem I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9) and can use Maple to simplify this to sqrt(25*cosh(4*t)^2) but I just can't see how that is done. (or how to get maple to show me the steps!) Can anyone help by showing the steps, including any...

Homework Statement Find the length pf the curve over the given interval. r=1+\sin\theta 0\preceq\theta\preceq\2\pi The Attempt at a Solution Ok I set it up as: 2\pi \int\sqrt((1+\sin\theta)^2+cos^2\theta) 0 and by simplifying and integrating, I get...

Homework Statement Find the length of the spiral of r=1/theta for theta\geq2 \pi Homework Equations \int\sqrt{r^{2}+r'^{2}} The Attempt at a Solution I thought of the formula for polar arc length, which is the integral of the square root of the sum of the square of r and the square...

So this seems to be a pretty straightforward question but I keep getting the arc length to be 0 and I redid this question many times.. Find the length of the parametrized curve given by x(t) =t^{2}-8t + 24 y(t) =t^{2}-8t -7 How many units of distance are covered by the point P(t)...

Homework Statement Given: R(t)= <(1/2)t^2, (4/3)t^(3/2), 2*sqrt(3)t> Find: Arc length function s(t) where t_0 =0 Homework Equations Is this the correct formula? ∫[0,t] sqrt( derivative^2 + derivative^2 +derivative^2) dt ∫[0,t] sqrt(t^2 + 4t + 12) dt The Attempt at a Solution...

Homework Statement A curce,C, has equation y=x^{\frac{1}{2}}-\frac{1}{3}x^{\frac{3}{2}}+\lambda where \lambda>0 and 0\leq x \leq 3 The length of C is denoted by s. Show that s=2\sqrt{3} The area of the surface generated when C is rotated through one revolution about the x-axis is denoted...