What is Arc length: Definition and 286 Discussions

1.Homework Statement y=x^{\frac}{1}{2}}- \frac{1}{3}x^{\frac{3}{2}}+\lambda For 0 \leq x \leq 3 Show that the arc length,s=2\sqrt{3} Homework Equations s=\int_{x_1} ^{x_2} \sqrt{1+ (\frac{dy}{dx})^2} dx The Attempt at a Solution \frac{dy}{dx}=\frac{1}{2\sqrt{x}} -...

I'm working on this problem x^5/6+1/(10x^3) [1,2] and I got the equation: sqrt(1+(5x^4/6-3/10^4)^2) or sqrt(1+25x^8/36+9/100x^8-1/2) I'm not sure how to integrate the last part, is there some sort of obvious substitution I'm missing?

It's easy question,but I don't know whether I solved it correctly. Homework Statement Calculate the length of the curve given by r=a\sin^3 \frac{\theta}{3} in polar coordinates. Here, a > 0 is some number. Homework Equations l=\int \sqrt{r^2(\theta)+(\frac{dr}{d\theta})^2}d\theta...

Can anybody help? Mathematical Physics. I'm seeking an analytical expression for the path length of a point that follows a helical path with the helix wound about an axis to form a torus. The arc path length of a helix is simple to compute, but when its formed into a torus there is a...

I need help with this homework problem: Making a turn, a jetliner flies 2.1km on a circular path of radius 3.4km. Through what angle does it turn? Any ideas that would help me in doing it?? thanks

Hi! Here's my question on finding arc length. If I've taken the derivative correctly, is there anyway I can simplify it before putting it into the arc length formula? Homework Statement Find the arc length where 0\leqx\leq2 y=(x^{3}/3)+x^{2}+x+1/(4x+4) Homework Equations...

[SOLVED] Arc Length Problem y=\sqrt{x^{3}} So you plug it into the formula for arc length. (integral of the sqrt of 1+y'^2) And it yields \int \sqrt{1+(\frac{3x^{2}}{2\sqrt{x^{3}}})^{2}dx From there you would use trig substitution, 1+tan^2theta = sec^2theta. But converting the dx to...

Is there a general formula for calculating the arc length between two points along an ellipse?

Homework Statement Find the point on the curve r(t) = (5Sint)i + (5Cost)j + 12tk at a distance 26pi units along the curve from the point (0,5,0) in the direction of increasing arc length. Homework Equations L = int (|v|) from 0 to T. The Attempt at a Solution T comes to be 2pi...

Homework Statement My book says if you write a plane curve in polar coordinates by p = p(?), a<=?<=b then the arc length is ??(p^2+(p')^2)d? (the integral is from a to b). It doesn't tell me how they got this equation though and I can't figure it out myself. what does the equation p(?) mean...

Guys, I need your kind assistance. I am studying arcs length. Suppose a vectorial function with domain [a, b] (interval in R) and range in RxR. This range is a curve in the RxR plane. Take a partition P of [a, b]: a= t0, t1, t2,..., tn = b. We have a straight line which goes from F(t0) to...

Homework Statement A cable hangs between two poles of equal height and 39 feet apart. At a point on the ground directly under the cable and x feet from the point on the ground halfway between the poles the height of the cable in feet is h(x)=10 +(0.4)( x^{1.5}) The cable weighs 12.5...

Homework Statement Just started Calc II last month, it's been smooth so far but I've run into a bit of snag involving the application of integrals in the calculation of arc length. The formula you use is the definite integral of (1+(d/dx)^2)^.5. Often once you derive the d/dx and...

1 Find the area bounded by the curve x = t - \frac{1}{t} , y = t + \frac{1}{t} and the line y = 2.5 . I know that A = \int_{\alpha}^{\beta} g(t)f'(t) \; dt I ended up with \int_{1}^{2} 2.5-(t+\frac{1}{t})(1+\frac{1}{t^{2}}) 2 Find the length of the curve: x = a(\cos \theta + \theta...

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'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...

\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...

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 +...

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...

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?

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

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...

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...