Deriving the Arc Length Formula in Calculus

[damian.gamlath]

The unfortunate epitome of modern-day tertiary education is "learn elsewhere but pay us anyway" - Patrick, you help maintain the status quo. Thank-you.

[Sabrina-scdb]

I'm procrastinating from doing my maths homework by watching your maths videos

[hubenbu]

This is my first math analysis lesson, it's beautiful.
There are so many brilliant and generous people out there.

[TooMuchTigerero]

I've been done with calculus classes now for almost two years but I still sometimes click on your videos just cause they're awesome! Keep up the great vids, students everywhere are grateful for your easy to understand/follow explanations!

[TheCutieEnity]

thank you patrick. I have graduated from university and your channel have been my savior!

[mariambobat]

Patrick : Ensuring that we pass our Courses.
You are the best.

[dvscrobe]

This was a very good explanation! I have a problem in Calculus where I was asked to find the distance traveled of a robotic joint. Used this to refresh on finding arc length of curve segments.

[tamircohen]

Can someone explain why the f(x_i*) turns into a regular f(x) in the last step?

[BlackCardvbs]

Patrick thanks for these lessons helped me with a lot of situations ...your the best

[doaard]

i passed math exam successufully with your lessons .thanks

[professorAP]

thanks a lot Patrick. you are the master of derivations

[mansurbhamani]

Perhaps you may make another video to find volume of Diesel Tank (cylindrical lying horizontal on the ground along it's length) as it gradually gets filled up at any instant.

[carloschuecos]

Patrick, all your videos are excellent. By the way, do you have something about deriving the radii of curvature?

Thanks for all your videos.

[BangMaster]

Hey Patrick, can you please do tutorials on Discrete Mathematics
it would be really helpful
thank you

[baselinesweb]

The whole part about the mean value theorem...could you replace that by dividing both delta X^2 and delta Y^2 (under the root) and then multiplying by delta X^2. You get the same result of 1+(delta Y/delta X)^2. Thanks for the video.

[herropaul]

I had just learned this yesterday in class lol

[ntruesdale]

This is my favorite application of Integral Calculus. Breaking up the curve, g(x), into segments allows use of the Pythagorean Theorem, provided they are short enough. Then the hypotenuse equals the segment. I write dl = sqrt (dx^2+dy^2). Then I just pull out a dx using distributive property and square root rule, sqrt ab = sqrt a x sqrt b. Then I have a product, f(x)dx = dl. Now integrate both sides. What is often overlooked, not understood, is that the summation is of area under a curve, not of lengths. Yes, we want to sum the segments, but Integral Calculus doesn't do that. It just sums areas, f(x)dx. Nonetheless, using just basic math, the integral can be formed. That's very cool, as is the fact that the length of the curve, g(x), is given by the area under another curve, f(x).

[victorserras]

Thanks for the rigorous demonstration; much better than khan academy's bs proof

[meganp]

exsubuy, whysubuy XD! great video thank you so much for explaining!

[anilkumarsharma]

if we have function and its derivative then we have a ration between them so we multiply this by 100 to find percentage, will this percentage gives some specific correlation between curve length of both or of function, if this method gives us some calculations then we will stop bothered about sharemarket updown