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 much will it have depreciated after 2 years, The value of a computer is...

The value of a computer is depreciated over ?ve years for tax reasons (meaning that at the end of ?ve years, the computer is worth $0). If a business paid $2,100 for a computer, ho

What is perfect squares, What is Perfect Squares ? Any number that can ...

What is Perfect Squares ? Any number that can be written as an integer to the power of two is called a perfect square. For example, 4 can be written as 2 2 4 is a "perfect sq

Permutation, explain the basics of permutation

explain the basics of permutation

HELP, a manufacturer is interested in developing a benefit segmentation of ...

a manufacturer is interested in developing a benefit segmentation of the cameramarket.suggest some major benefit segments with market targeting strategies.

Free - undamped vibrations, It is the simplest case which we can consider. ...

It is the simplest case which we can consider. Unforced or free vibrations sense that F(t) = 0 and undamped vibrations implies that g = 0. Under this case the differential equation

Statistics, The winning team''s score in 21 high school basketball games wa...

The winning team''s score in 21 high school basketball games was recorded. If the sample mean is 54.3 points and the sample standard deviation is 11.0 points, find the 90% confiden

How many hours will it take before the cars are 610 miles, Two commuters le...

Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli

Give examples on multiplication rule in probability, Example: Suppose your...

Example: Suppose your football team has 10 returning athletes and 4 new members. How many ways can the coach choose one old player and one new one? Solution:  There are 10 wa

What is the width of the walkway in feet, A garden in the shape of a rectan...

A garden in the shape of a rectangle is surrounded through a walkway of uniform width. The dimensions of the garden only are 35 by 24. The field of the garden and the walkway toget

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