# Arc length

##### Intros

##### Examples

###### Lessons

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

Instead of finding the area under the curve, we are going to be the length of the curve between a and b. Now we know we can find the length of a line using the distance formula, but what about the length of the curve? In the intro video, we will learn that we can find the length of the curve by manipulating the distance formula into an integral. After, we will be applying the formula that we've found by finding the arc length of functions in terms of x. We will then look at some advanced questions where we will find the arc length of functions in terms of y, as well as finding the arc length function with an initial point.

The arc length of a curve from a to b:

$Arc\; Length = \int_{a}^{b} \sqrt{1+[f'(x)]^2}dx$

Arc length as a function of a variable, x:

$s(x)=\int_{intial}^{x} \sqrt{1+[f'(u)]^2}du$

Arc length as a function of a variable, x:

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today