Arc Length | Calculus 2 Lesson 6 - JK Math

How to Calculate Arc Length Using Definite Integrals (Calculus 2 Lesson 6)

In this video we look at how to use definite integrals to calculate the arc length of curves with respect to x and with respect to y. The process is similar to calculating the distance between two point or the length of line segments in algebra with the distance formula, except this concept is extended to a calculus setting.

This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 Determining the Arc Length Formula
6:56 The Arc Length Formula
7:43 Example 1 - f(x)=2x+1 from x=0 to x=3
10:14 Example 2 - g(y)=2/3(y-1)^(3/2) from y=1 to y=9
15:48 Example 3 - y=(3/2)x^(2/3) over [0,8]
27:02 Outro

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-Josh from JK Math

#calculus

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[berzi]

i dont comment much, but you have been such a huge help in me passing through my calc 2 class currently. The explanation, the quality, its really like a gem. I know you have been making such good vids for a long time and not getting the views you deserve, and I hope you continue making more vids of calculus and beyond and one day i hope it will be worth it, all the time and effort you put in and all the struggle.
Thank you.

[malldvd]

Im glad I found this channel. It made me realize that font can play a big role in absorbing the information. The rounded strokes make calculus feel less intimidating.

[AnnakaReed]

I just really wanted to say thank you this is the best math channel on youtube!

[Wunjogenius]

holy shit, this is a way shorter explaination for the formula than the professor leonard's one. thanks

[Tivnanmath]

I got a bit uneasy on the last example b/c you left the lower and upper limits as the x values 0 and 8 when you expressed the integral in terms of u. I thought you were going to plug those in, but then you changed it all back in terms of x and it was worked out. I tell students to write x=0 and x=8 if they choose to go back to the x world. I find it a bit easier to to use u=1 and u=5 to evaluate the integral. No harm no foul though, but it does lead to confusion when x and u appear in the same integral.

[sommerray]

Why dont square root and square just cancel, and you just deal with multiplying it out