Arc length with polar coordinates, Mathematics

Assignment Help:

Arc Length with Polar Coordinates

Here we need to move into the applications of integrals and how we do them in terms of polar coordinates.  In this part we will look at the arc length of the curve specified by,

r = f (θ)

α < θ < β

where we as well assume that the curve is traced out precisely once. Just only as we did with the tangent lines in polar coordinates we will very first write the curve in terms of a set of parametric equations,

 x = r cosθ

= f (θ) cosθ

 y = r sinθ

= f (θ) sin θ

and we can now make use of the parametric formula for finding the arc length.

We'll require the following derivatives for these computations.

dx/ d θ = f' (θ) cosθ - f (θ) sinθ

= dr/dθ cosθ - r sinθ

 dy/dθ = f' (θ) sinθ + f (θ) cosθ

= dr/dθ sinθ + r cosθ

We'll require the following for our ds.

476_Arc Length with Polar Coordinates.png

After that the arc length formula for polar coordinates is,

Where

L = ∫ ds

ds = √(r2 + (dr/dθ)2) dθ


Related Discussions:- Arc length with polar coordinates

Differentiation, Need Solution Find (dy)/( dx) for; (i). y = x 7 ...

Need Solution Find (dy)/( dx) for; (i). y = x 7 (ii). y = x 2γ (iii). y = x -3 (iv). y = x

Repeated eigenvalues, It is the last case that we require to take a look at...

It is the last case that we require to take a look at. During this section we are going to look at solutions to the system, x?' = A x? Here the eigenvalues are repeated eigen

Vectors, calculate the vector LM given l(4,3),m(-1,2)

calculate the vector LM given l(4,3),m(-1,2)

Polynomials in two variables, Polynomials in two variables Let's take a...

Polynomials in two variables Let's take a look at polynomials in two variables.  Polynomials in two variables are algebraic expressions containing terms in the form ax n y m

Determine the probability, An insurance company/organization takes a keen i...

An insurance company/organization takes a keen interest in the age at which a person is insured. Thus a survey conducted on prospective clients indicated that for clients having th

Transportation problem, 12. List the merits and limitations of using North ...

12. List the merits and limitations of using North West corner rule.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd