arc length of a vector function (KristaKingMath)

In this video we'll learn how to find the arc length of a vector function when the vector function is given in terms of a parameter value t, where t is defined over a closed interval.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[MrYeahRiiight]

Thank you for not doing a problem with the trig identity like so many others. This helped me so much more.

[joeynoonan]

10 years later, your videos are easier to understand then my professors and other examples online, well done truly and thank you very much. Your notes and explanation are crystal clear and that's the key to understanding math for those who can't read it or do it well!

[scotthackney]

You have the best videos for calculus 3 on YouTube by far, they've been helping a lot with my homework this semester. Thank you!

[Primitive_Code]

For a while, I was like; please don't forget the 2 under the square root. Then you showed how it was part of a perfect square root. Thanks for sharing this difficult arclength in space example.

[srijaksingh]

your videos are soo easy to understand and really a lot helpful

[MrScorpiofire]

you have a lovely voice, very informative video, thank you :, )

[financewithsom]

thanks mam your lecture helped me a lot

[mikennarenedew]

thank you!! does it make a difference if the interval is from -infinity to infinity?

[sheet-son]

We just started related rates and I'm having a bit of trouble. Can you maybe do a few of them? Like the pond ripple area rate of change, and the falling ladder? I have a decent grasp of those, but the ones where a cone is being emptied or filled leave me scratching my head. Thanks :)

[ExCoSeH]

the square root of a perfect square will always be positive. So you should've taken the absolution value, right?

[SoMoeYourToe]

Lmao this exact problem was on the calc 3 exam for last semester

[Ensign_Cthulhu]

At 7:15 isn't your integral, L, also equal to Int[2*sinh(t)].dt ?

[matrixate]

I've never heard of a multiple-choice test in calculus.

[elijahkwalozy]

The derivative of square root of 2t how did it come jst square root of 2 help here

[elijahkwalozy]

The derivative of square root of 2t how did come jst 2 help here

[MyNameIsTwitted]

shouldnt there be +1 under the root???