Introduction to Line Integrals - Focus on Parameterizing Curves

[@NakiaRimmer]

@12:20 : r(t) should have 3-4t in the first component

[@sophiebaird3400]

Thank you SO much! Things that have confused me for a long time finally click when I hear you explain them!

[@NakiaRimmer]

Thank you‼️

[@CaptainBobSim]

You are an outstanding teacher! Thank you for this video!

[@adithyarajapakshe3791]

wow! well explained and helpful, thanks, Mr.Rimmer!!

[@anysianas5099]

you saved my semester I was about to drop my class because it did not understand parametrization

[@louismotte5079]

thank you mr Rimmer very helpful, and i am glad to have found your videos :)

[@muwongeevanspaul9166]

Am so greatiful, thanks so so so so much....I have clearly understood line integrals....

[@Pozizzle]

Fantastic explanation!

[@jam9339]

sobrang maestra ito

[@ryandick7264]

Fantastic video, I never really understood parameterization from Calc 2, and was clueless when the line integral appeared in Calc 3. You've helped me pass

[@gregorypayton8308]

sameeee

[@JMissEscobedo]

Literally my life right now.

[@henriquenunes7196]

Great video😊

[@azizkash286]

amazing video sir

[@elpatron8375]

Great video, very well explained and very helpful as well, thanks!

[@toniocartonio572]

Hi, how do you parametrize a vertical line? Great vid btw

[@NakiaRimmer]

Hello! Great question. In 2 dimensions a vertical line has equation x = k for some constant k. There is no mention of y in the equation at all. This means that y is free to be anything you want but x is stuck on k. So you would parametrize it by have x = k and y = t. You would allow t to go from your smallest y to your largest y if it is a line segment. If it is the entire line, then t would go from -infinity to infinity. Let me know if you were asking about a vertical line in 3 dimensions.

[@toniocartonio572]

@@NakiaRimmer Yes, I was asking in two dimensions, thanks. And if the parametrized line, for example, starts from (2;2) and ends in (0;2), how would parametrize it? Is it y=2, x=t?

[@NakiaRimmer]

@@toniocartonio572 Yes, but the issue you run into is that t starts at 2 and end at 0. t is going backwards, usually you want t to go forwards. What you can do is let x =-t and then t would go from -2 to 0. The thing with parametrizations is that there is no unique way to do it, so you should parametrize whichever way is easiest for you.

[@bgvlogs6601]

For the ending isn't x=3-4t why did you put 3+4t in your parameterized vector r(t)= < 3+4t, 2+6t, 1+6t > ?

[@NakiaRimmer]

Yes, thank you for catching that mistake. I’ll pin a comment with the correction.