Arc Definition and 485 Threads

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...

Homework Statement volumetric modulated arc therapy (vmat) is a new technology in radiation therapy. It gives radiation treatment in a single 360 degree or less arc. During VMAT delivery on medical linear accelerator dose rate, gantry speed and MLC shapes can be simultaneously varied when...

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 There is an arc with an angle of 2\alpha and radius R What is its center of mass. (It is implied that it is to be measured from the center of the circle the arc is a part of.Homework Equations Integration, trigonometry.The Attempt at a Solution Well, the formula for a center...

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 arc x = 3y^ (4/3) - 3/32y^(2/3) and y lies between 0 and 216 Homework Equations l = integral sqrt (1 + (dy / dx )^2) The Attempt at a Solution after integration i got this y + 3/16y ^(-4/3) / (-4/3) i have to apply 0 and...

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 Im having trouble figuring out which equation to use for this problem. The problem states: "Consider a pilot at the lowest point of a circular arc banking upward. Find the tightest radius arc that an untrained individual can fly ( a total of +5 G, G standing for the normal...

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...

Hello, This is my first post, so please forgive me if this has been covered before. In my searches I was unable to find any previous threads specifically about this question. I made a statement in a link sharing forum that was immediately disputed. I'm not interested in winning an argument so...

Let C be the curve obtained by intersecting the sphere x^2 + y^2 + z^2 = a^2 with the surface root(x^2 + y^2)cosh(arctan(y/x))=a. Find the length in the first octant that joins the points A (a,0,0) and B(x,y,z). Im not sure what to do. Should i change it into different types of coordinates?

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 = "...

(F) Thanks in advance (F)

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...

Hello, I am trying to find an estimated value (or range) for the current of an electric arc. I imagine this may be a function of the voltage producing the arc, the distance between the electrodes, and other parameters. If this is true, then take the voltage to be around 80kV and the...

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...

Homework Statement Here, I have two ways of finding the y-coordinate centroid of a semicircular arc using polar coordinates. First one is considering a circle of radius a, centred at the origin. What I have done is \int ds = \int_0^{\pi} a d\theta = \pi a and then \int y ds = \int r^2 sin...

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...

Gas core reactor rockets use nuclear gas reacting to super heat and therefore pressurize hydrogen. They operate at about 25000 C. Why not use a high intensity plasma arc which routinely operate at about 13,000 C but if designed to can go much higher by at least several fold. I got bored...

Homework Statement Let C be the arc of y=x2 from (0,0) to (1,1). Evaluate \intxdxHomework Equations C1: x=t y=t2 -1 \leq t \leq 1 so -1 \leq x \leq 1 The Attempt at a Solution dx is x' dt, right? For some reason, I just can't figure this out. Any help?

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 = sin \pix Using arc length and surface revoultion on x-axis 0 <= x <= 1 The Attempt at a Solution d/dx sin \pix = \pi cos \pix (\pi cos\pix)^2 = \pi^2 cos^2\pix \int sin pi * x * 2 * pi * \sqrt{1 + pi^2 * cos^2 (pi*x)} u = pi cos (pi * x) du = -pi^2 * sin...

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...