Parametric Curves - Calculating Area

[cheeserice123]

i has a question, does x = T or theta for any type of parametric equation? if so, why?

[earthyearth]

@earthyearth at 5:04

[HoorayBier]

Wouldn't at t=0 the curve be undefined?

[WallyTheBand]

AAAAaaaaaaaahhhhhhhhhhhhhhhhhh­hh dx = (1 + t^-2)dt

Ok, I'm over it.

[subarashi13]

i know that im late but why t is from 1/2 to 3/2?isnt ir from 1/2 to 2?

[kevinj888a]

why in the first formula of integration you write g(t) x f'(t) but in your work, you use 2.5 - y??

[saraelleese]

how do you decide which is g(t) and f(t) ? or is traditionally just f=x, g=y? i also wish you made physics videos :(

[killaDandM]

I definitely think you are better than the Khan Academy guy.. I'm with deonjo

[MrArod21]

Thank you, now I am going to pass my test!

[tokyo200]

excuse Patrick but are you using the textbook "Essential Calculus: Early Transcendentals" by James Stewart?

[patrickJMT]

@tokyo200 no, but one of the books i have around is by stewart

[tokyo200]

@tokyo200

Oh, okay then.

The reason why I ask is because most of the problems you are using is exactly like my homework problems LOL.

By the way, you are a great teacher.

I know that sounds very cliche, but I just wanted to point that out to you.

Hope life's okay. :)

[FMAZON3]

@tokyo200 expensive book

[macrod15]

@FMAZON3 not on amazon, saves so much

[ShinobiBoiX]

lmao i have a problem set im going crazy over and i had this exact problem left last to do

[Morelloo1]

Ok so what happens when you need to find the volume with parametric equations. More specifically the volume of an elipse. I was thinking taking the area of an elipse and multiplying it by the integral e.g integral sign PiAB*G(t)*F'(t). I havent been able to find much on ellipses and it gets confusing.  Finding the area is easy just volume is hard.

[rubywolf999]

youre my hero patrickJMT

[bf2gamestotal]

amazing channel

[sncho143]

is there any chance u can make a video on Parameterized curves or parametric equations in three dimensions

[fatmoe92]

DUUDE UR THE MOST AWESOME PERSON I HAVE EVER MET IN MA WHOLE LIFE

U SAVED MA LIFE MAN !

I HAD A FINAL FOR TOMMOROW AND I HAD NO IDEA ABOUT ANYTHING AND U MADE ME UNDERSTAND THANK GOD U EXIST MAN !!

[Ssendecki]

@fatmoe92 wake up

[Alexihi]

Hi, iv had a lot of trouble with this problem. find the area of

x=acos(theta) y= bsin(theta) 0 =< theta=<2pi

[crazypak11]

how would i solve this parametric equation using X

Find the area bounded by the curve x = cost, y = sint, where 0 ≤ t ≤ p

Method 1: Eliminate the parameter t, and find the area that involves only with x.

[StoggyDyle]

He is better the Khan Academy, more common sense examples, thanks for all the hard work.

[kowsco]

wow these helped more than my prof lol spent 2 hours trying 2 learn this

[miphone69]

for persons who would not pick up on 2 being a solution for the equation y = t + (1/t) you could multiply the equation (t^2 -2.5t + 1 = 0) by 2 thus giving an easier equation to factorize and solve. ie (2t^2 -5t + 2 = 0)

[ifonly4]

where have you been all my schooling?

jk jk

[ifonly4]

very detailed and thorough; thank you :)

[aboyandastang]

Amazing thank you! better than my calc 2 teacher ..

[deonjo]

I think you are cooler than the Khan Academy

[patrickJMT]

hahahah

[skyfaze]

lol agreed (Y) for sure the khanacademy guy gives me a creepy feel

[zndr27]

@deonjo dont be hating! they're both cool

[patrickJMT]

@zndr27 sal at ka's is doing great stuff : ) i am flattered that many of you like my stuff better though! i think we are both trying to accomplish slightly different things, so it is good in that respect.

[TheWiseGeek]

@deonjo haha yeah man, Khan academy is good, but his lessons are for pre-schoolers..PatrickJMT you rock!

[patrickJMT]

@TheWiseGeek plenty of room for all styles : ) he got a $2,000,000 grant, so i am just happy to hear us being compared. hopefully something will come my way one day! : )

[Finalseeds]

I tried to find finding area enclosed by loops of the polar curve on the website and here but couldn't find it. How would somebody go about in finding it?

[patrickJMT]

yea, i do not have a video for that yet... maybe i will make one later!

[maybeok1]

Please do....THANK YOU!

[nanohark]

Patrick, i have to point out the same thing as jdexo04. The values of integration are t=1/2 to t=2, so you might wanna put a note in there so pple dont get confused. Great vida anyways! Thx again<!

[patrickJMT]

i thought i had put in some annotations, but i forgot!

soooooo, they are now there! thanks for reminding me. hopefully i have not confused too many people!!

[bharathsf]

@nanohark thanks for the update..i thought we have to integrate from x=-1.5 to x=1.5 for some weird reason..

[kj0965]

you are calc god!! thank you so much!

[panda360]

very good

[univasa]

This helped a lot, but do you have any videos on calculating area outside the inner loop and within the outer loop of polar curves like r=sin2@+2?

[patrickJMT]

great! glad to help!