Arc Length of A Polar Curve (proof)

Arc Length of A Polar Curve,
Calculus 2

[blackpenredpen]

Best of luck on the final, my summer calc 2 students!

[SigSelect]

We have so much technology, so many tricks to learn, so many ways to represent things, but a man in front of a whiteboard still manages to be the best resource for really learning and engaging with the math that students recognize as important. Thank you for your work, I hope teachers everywhere are inspired.

[benjaminbrady]

What they teach you in class: integrate 2x
What they put on the test: derive the arc length of a parametric equation formula

[easygoing]

When you have no idea what is going on but you watch it anyway...

[neilgerace]

2:40 What's the product rule? I have always used the Prada Lu instead :)

[turtlellamacow]

There is an easy "intuitive" way to remember this that you might want to show (it makes the formula derivable in a second). Resolve an infinitesimal length of curve into its components in the radial direction and the theta direction. The first one has length dr, and the second has length r*d(theta) (arc length formula). Hence dL = sqrt(dr^2 + r^2 d(theta)^2) ----> your result

[hdheuejhzbsnnaj]

Thank you, my book (like most) just glosses over everything and gives the final formula which does students a disservice.

[sumoman]

This was exactly what we needed. Thank you!

[ivanjanka]

Thank you so much! Love your simple explanations! I just realized how calculus is beautiful but our uni proffesors failed to show us that

[mohamedmahl]

Best of luck on the final we all with u

[valengo]

I really need proofs for formulas so thank you!

[VibingMath]

Great proof! Good luck to those who will have final!

[Joseph-tmvv]

I’m so glad that I was able to follow a blackpenredpen video

[jayapandey]

All I was waiting for -
Wouldn't it be nice ....

[aryanjoshi]

Actually I liked your video too much /(love from India 🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳)

[TN-whyf]

Thank you man
That was really helpful

[vincentespe]

Hey Blackpenredpen. Can you do a series on doinh engineerinh problems with integral or differential equations? thanks.

[alejrandom]

I |love| everytime he says squaaare root

[cameronspalding]

Using Lagrange’s Version of Taylor’s Theorem; you can prove that the absolute value of the sum from k=n to infinity of x^k/k! Is less than or equal to exp|x| * |x|^n/n!
Do a video on this

[willyou]

What if the limits are the same, ie i'm integrating over a loop.

the arc length is certainly not 0, but equal limits means integral is 0?