Worked example: arc length | Applications of definite integrals | AP Calculus BC | Khan Academy

A finely tuned example demonstrating how the arc length formula works.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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[aidansmith]

My professor's teaching online for the semester so she can just reuse all her old videos from the last 3 semesters. This 15 minute-series explains everything way better than her 30-minute video could ever hope to

[pepegpala]

some times i hate math, i come here, back to being a lover.

[DonOtto]

I like how you write your radicals, I might have to adopt that

[leonidesubackup]

this is perfect for before test review!!

[bolis]

why do we change the boundaries of the definite integral? is it because we used u-sub?

[neelmodi]

Thank you so much I understand how to do it now!

[HimanshuSoni_Axelerate]

Please someone tell me which application is used by Sal, besides using Bamboo tablet? Not the recording app, but the app that Sal uses to write on? Is it Smoothdraw?

[AVSbeats]

Who pauses the video to work on it 👁 👁

[renzoandre]

What conceptual proof video from before is he talking about? I must see it.

[liskyu]

Isn't there suppose to be a 2Pie in front of the integral? Or is that only for finding the surface area of the arc?

[qualquan]

Pretty good but hesitates to call ds a tangent since he thinks like others that a tangent is a point with no length. Used the term "loosey goosey" when deriving the ds formula (ha ha).
Yet they integrate tangents to get length of a curve.

[linkster]

at 2:15 cant we just leave it as √(1+((3/2)x^(1/2))^2)? that way the square root cancels out the square so we would just have to integrate 1+(3/2)x^(1/2)?

[ricjadelacruz]

Isn't it 8 when we multiply (32/9)(9/4)?

[anthonycarroll]

when i did the u sub for the bounds i got u = 8 not 9

[jahidurjaman]

If f(X)=x^2 then find the length of arc

[ptyptypty]

so, I can throw away my abacus now? :)

[adibzinnurine]

4:27 Me be like: What? Dealing with me?

[alex-dnto]

what i wanna duuu ( derivative of d with respect to u joke)

[lexinaut]

The Ghosts of Departed Quantities (that is the differentials) would approve, I think. Very nice if infinitesimally quirky presentation.

[liskyu]

Isn't there suppose to be a 2Pie in front of the integral? Or is that only for finding the surface area of the arc?