Arc length formula - applications of integrals, Mathematics

Assignment Help:

Arc length Formula

L = ∫ ds

Where

ds √ (1+ (dy/dx)2 ) dx                                     if y = f(x), a < x < b

ds √ (1+ (dx/dy)2 ) dy                                     if x = h(y), c < y < d

Note that there is no limits were put on the integral as the limits will depend on the ds that we are using. By using the first ds will need x limits of integration and by using the second ds will need y limits of integration.

Idea of the arc length formula as a single integral with dissimilar ways to define ds will be suitable when we run across arc lengths in future sections. As well, this ds notation will be a nice notation for the later section as well.

 


Related Discussions:- Arc length formula - applications of integrals

How to adding rational expressions with common denominators, Adding Rationa...

Adding Rational Expressions with Common Denominators To add or subtract fractions or rational expressions with common denominators, all you do is add or subtract the numerators

Theorem of reduction of order, In this theorem we identify that for a speci...

In this theorem we identify that for a specified differential equation a set of fundamental solutions will exist. Consider the differential equation  y′′ + p (t ) y′ + q (t

Solution of rectilinear figures, A tower and a monument stand on a level pl...

A tower and a monument stand on a level plane. the angles of depression on top and bottom of the monument viewed from the top of the tower are 13 degrees and 31 degrees, respective

Areas of a rectangle, a rectangular field with a path around it measures 1...

a rectangular field with a path around it measures 120m by 50m.if the path is 1m wide all around,(a)find the length of the outer edge of the path.(b)find the area of the path

Explain how we converting fractions to percents, Explain how we Converting ...

Explain how we Converting Fractions to Percents ? To convert a fraction to a percent: 1. Convert the fraction to a decimal using long division. 2. Move the decimal point two p

Rational, how can you identify if a certain number is rational or irrationa...

how can you identify if a certain number is rational or irrational?

1, how do you find the perimeter of an equalateral triangle

how do you find the perimeter of an equalateral triangle

Elli[ital paths of celestial bodies, Create a detailed diagram to describe ...

Create a detailed diagram to describe the equation of an ellipse in terms of it’s eccentricity and indicate how the foci and major and minor semi-axes are involved. Y

Proof for absolute convergence - sequences and series, Proof for Absolute C...

Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign.  The meaning of this is that we can then say, 0 a n +

what fill amount are they searching, Brewery has 12 oz bottle filling mach...

Brewery has 12 oz bottle filling machines.  Amount poured by machine is normal distribution mean 12.39 oz  SD 0.04 oz. Company is interested in in reducing the amount of extra beer

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