Area Between Curves - Integrating with Respect to y

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  • เผยแพร่เมื่อ 7 ก.พ. 2025
  • Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Area Between Curves - Integrating with Respect to y - I show the general formula, graph two functions, and set up the integral in this video.
    I calculate the integral in part 2!
    For more free math videos, visit PatrickJMT.com

ความคิดเห็น • 122

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +20

    find points of intersection, take a point in-between, use the larger value

  • @katakuriplays6687
    @katakuriplays6687 6 ปีที่แล้ว +14

    Thank you patrick!!! Way back in 2014 when Im taking up differential and integral calculus.. This video saved me. Now Im an engineer all thanks to you and all the videos that you'ved made!! Thank you from the bottom of my heart sir!!

  • @isaiahcruz
    @isaiahcruz 11 ปีที่แล้ว +9

    Have an exam tomorrow, and I always come here for my review. Helps so much!

  • @lowisl289
    @lowisl289 7 ปีที่แล้ว +52

    I think that the most difficult part is the sketching graph part. once u draw the right graph, its easy to execute

  • @wajeehazaheer7812
    @wajeehazaheer7812 8 ปีที่แล้ว +9

    My final exam is tomorrow and I can safely say that with the help of your amazing videos I think I might actually do well!!!!!!! Thank you PATRICK JMT you are a real MVP

  • @kalebscott282
    @kalebscott282 4 ปีที่แล้ว +7

    Bro I was 6 when this came out and now I'm watching it for help in my calc II class in college.

    • @jensmalzer6344
      @jensmalzer6344 3 ปีที่แล้ว +1

      I wasnt born yet and im using this for ap calc

  • @engineernael2567
    @engineernael2567 11 ปีที่แล้ว

    i was thinking of taking a tutor but with patrick jmt videos... believe me there is nooooo need. he makes every things clear and simple...thanks

  • @masterlordLOVER
    @masterlordLOVER 12 ปีที่แล้ว

    man ... ur the most awesome teacher ever .. i have a midterm in two days and i didn't go to a single class this semester.. I thought i will fail in this subject however, u gave me a hope.. after watching most of ur videos " about 5 hours " i could solve the midterms sample relatively easy .. thank you so much Wish u all the best..

  • @DaddyDix92
    @DaddyDix92 16 ปีที่แล้ว +2

    Great video. I always look at your videos before I go to class to set a base for understanding concepts because you very good at explaining in a simplified manner. Thank you.

  • @katielafa
    @katielafa 12 ปีที่แล้ว

    Your videos are an outline of my book. It's almost like you can made these videos to go along with my class. You are my hero.

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +1

    you are only looking at the finite region trapped by the two curves. over that small region, 1-y^4 is further to the right

  • @MundusLitterae
    @MundusLitterae 15 ปีที่แล้ว +1

    Think about it this way. Which graph lies to the right most. In this case, it would be the graph 1-y^4 because it's the right most when you graph it. Do you mean what I mean? At least at the part where you're determining the area between the curves.

  • @birdman1265
    @birdman1265 11 ปีที่แล้ว +1

    Pattrick you are a really smart man. Thanks for the videos.

  • @kyachimegann
    @kyachimegann 14 ปีที่แล้ว

    Thank you so much for these videos. I would've failed this semester of calc without them---my teacher understands what he's teaching but doesn't seem to understand that he doesn't communicate it clearly (i.e. not explaining steps he didn't write down, not always explaining the strategies to use for solving specific problems, etc.) and the book we have doesn't have enough complicated examples to help with the problems we do for homework and the tests. I feel like you were my actual teacher, lol

  • @paulbird27
    @paulbird27 13 ปีที่แล้ว

    You are saving me a lot, thanks to you my last test was pretty high, im hoping it would help too

  • @willemthaetsi4043
    @willemthaetsi4043 10 ปีที่แล้ว +1

    You are over the moon man,I like your videos big time.

  • @tjerriam
    @tjerriam 11 ปีที่แล้ว

    my friend told me that she made a separate account in youtube just to watch your tutorial videos haha..
    nice idol patrick! XD this video really helps =)

  • @ellikadan2x
    @ellikadan2x 14 ปีที่แล้ว

    Thanks for helping me pass everytime we have a quiz!

  • @B.A.Gondal
    @B.A.Gondal 11 ปีที่แล้ว +20

    WOW 1440P....way to go patrick

    • @MashrufKabir
      @MashrufKabir 10 ปีที่แล้ว

      what..

    • @B.A.Gondal
      @B.A.Gondal 10 ปีที่แล้ว

      ***** Resolution.

    • @MashrufKabir
      @MashrufKabir 10 ปีที่แล้ว +1

      I know.... but it seems pretty clear though.

    • @B.A.Gondal
      @B.A.Gondal 10 ปีที่แล้ว +1

      lol no no....if you watch this video in flash player instead of HTML player...You will see resolution up to 1440P which is essentially 4K...and this is quite rare with videos and is only limited to high end stuff YET....but Patrick's video is appearing in 4K thats why i made that comment

    • @MashrufKabir
      @MashrufKabir 10 ปีที่แล้ว

      Oh alright man. Sorry I didn't get it at first!

  • @harrymax8072
    @harrymax8072 10 ปีที่แล้ว +6

    Why did he solve for y=0 to find the points of intersection? As opposed to setting the two equations equal to each other? (Same result I know but unsure why)
    Thanks team - pat your a legend

    • @blackprince681
      @blackprince681 8 ปีที่แล้ว

      same problem here why did he make x=0 and not x=x so 1-y^4=y^3-y but in that case how could we solve the equation so please if someone can explain

    • @tomatrix7525
      @tomatrix7525 4 ปีที่แล้ว

      It’s just different ways of doing it... if he did it your way you could equally ask why he didnt do it the other way. Also, his way wiill finds three poinys, the third at 0,0, but if we tried your way we would only get two, where they intersect twice... so his way is a bit more effective in that sense...

  • @Jnorrisclay
    @Jnorrisclay 14 ปีที่แล้ว

    thank you SO SO much for these amazing vids. Theyve helped me so much!! just got a 103% on my calc test :)
    thanks again~

  • @minusjason
    @minusjason 14 ปีที่แล้ว

    Thanks for your video. I'm reviewing this stuff and it's helpful. At about 4:05, I think you meant to say "We'll figure out now where x equals 0," rather than "y."

  • @p3destrian
    @p3destrian 15 ปีที่แล้ว

    thank you!!!!
    patrick you are the BEST

  • @rsadsultanov3071
    @rsadsultanov3071 5 ปีที่แล้ว +1

    it still helps thans very much for efforts

  • @llx2o1
    @llx2o1 13 ปีที่แล้ว

    @Billabong024 the problem stated x = y^3-y.... if its x= then you integrate with respect Y, if its Y= then integrate respect to X.....

  • @rudeliorodriqueziii1090
    @rudeliorodriqueziii1090 7 ปีที่แล้ว

    Thanks for the video! Great job man, I really appreciate it!

  • @destinysense
    @destinysense 7 ปีที่แล้ว +17

    I can smell the Expo marker from here

  • @NaytTheGrayt
    @NaytTheGrayt 12 ปีที่แล้ว

    Patrick JMT... now in stunning HD!

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว +1

    @Jnorrisclay nice grade : ) keep up the good work!

  • @Makeanimagination
    @Makeanimagination 12 ปีที่แล้ว +2

    So, can you tell me that when I integrate with respect to x it's almost the same when I integrate with respect to y?

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    good luck!

  • @jzen2016
    @jzen2016 12 ปีที่แล้ว

    Midterm tomorrow, PatrickJMT today :)

  • @dreamlanddon
    @dreamlanddon 8 ปีที่แล้ว

    I admire your work too much teacher.... It's a lot worthy

  • @x4812k
    @x4812k 16 ปีที่แล้ว

    that's a very good idea. I think I'll start doing that instead of scrambling to watch them the night before a test, haha.

  • @JMelodic
    @JMelodic 15 ปีที่แล้ว

    how do you decide which is the left-most or the right-most function? or does it not matter which you subtract from which?

  • @raejohnson2647
    @raejohnson2647 8 ปีที่แล้ว

    Thank you.

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @babicz good luck!!

  • @nabilalmarfadi7748
    @nabilalmarfadi7748 9 ปีที่แล้ว +206

    who thinks that he or she isnt going to pass calculus II :p

    • @slowbros1048
      @slowbros1048 7 ปีที่แล้ว +1

      66 likes lmao

    • @pogarythm4373
      @pogarythm4373 6 ปีที่แล้ว +2

      So did you pass?

    • @jaffermohammed3787
      @jaffermohammed3787 6 ปีที่แล้ว +4

      I think he did
      it seems easy but during the test we cannot solve anything

    • @tomatrix7525
      @tomatrix7525 4 ปีที่แล้ว

      It really isn’t too bad.. Main things to remember is that you can integrate in respect to Y, most people dont know this. Here for e,g, a y integration makes it easier than X. Sketch graphs for a visual, and then use your formula...

    • @kalebscott282
      @kalebscott282 4 ปีที่แล้ว

      I'm 4 years late but me!

  • @kcgotfre
    @kcgotfre 11 ปีที่แล้ว

    you're left handed like me! :D haha having fun with that whiteboard? Thanks for the help!

  • @ShuyanStoryTeller
    @ShuyanStoryTeller 8 ปีที่แล้ว

    many many thanks.

  • @aihaibara3926
    @aihaibara3926 8 ปีที่แล้ว

    thank you. you explain it very clear but i have problem in drawing the graph.

  • @glitterdust04
    @glitterdust04 8 ปีที่แล้ว

    you're awesome! Very helpful thank you :)

  • @Billabong024
    @Billabong024 13 ปีที่แล้ว

    how do you know if you HAVE to integrate with respect to y? I don't quite understand the part when he said chopping the integral apart into two pieces

  • @sabianhhxevolution
    @sabianhhxevolution 12 ปีที่แล้ว

    why is x = 1-y^4 the right most? it seems to me that x = (y^3-y) extends much further to the right than the other function.

  • @sunshinecake1
    @sunshinecake1 12 ปีที่แล้ว

    how do you find the right most and left most if the fn is slightly more complex and you don't have time to graph it? obviously it's the one that's bigger, but I never learned how to figure that out...

  • @tmrcdo07
    @tmrcdo07 13 ปีที่แล้ว

    Wow!!! Thanks a lot!! You actually helped me a lot. Just to let you know. :D

  • @nopitain1195
    @nopitain1195 6 ปีที่แล้ว +1

    how do you know whether to use dy or dx to find the area b/w 2 curves?

  • @animelovergonemad331
    @animelovergonemad331 12 ปีที่แล้ว

    I am now expressing my love for you.
    THANK YOU!

  • @isabellapena3113
    @isabellapena3113 2 ปีที่แล้ว

    You can tell they won’t “criss cross” because they’d have to have a third point where they’re equal to each other for that to happen!

  • @AuburnOutcast4
    @AuburnOutcast4 11 ปีที่แล้ว +1

    6:20 "make sure my graph's not totally crazy." Never did I encounter one single graph in Maths that is not crazy -_-

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @MzVixen05 practice practice practice!

  • @craig7878
    @craig7878 2 ปีที่แล้ว

    Hi! How can I find the intersection when I have been given once function x = y^2 and another function y = 3x-2. I have two functions that are with respect to different variables... What is the method for that?

  • @SPBigJoe
    @SPBigJoe 16 ปีที่แล้ว

    How would you find the region bounded by y=x**2, the tangent line at (1,1), and the x-axis?

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    beats me

  • @flamesk8er5
    @flamesk8er5 12 ปีที่แล้ว

    How did you do in college on calc tests? I feel like I know the material very well but I only get 85s or so because of stupid mistakes because I am nervous when i am taking the tests. Like I can do most things easily but lets say i take the sqroot i forget to make it +/- so i lose points :/

  • @fowz2073
    @fowz2073 7 ปีที่แล้ว +1

    what i didn't get is how to find the points that you gonna subs at the end . when is not given

  • @wazgood121
    @wazgood121 11 ปีที่แล้ว

    have you done any video on this subject with trig functions?

  • @amithvalentine1479
    @amithvalentine1479 10 ปีที่แล้ว +6

    How do we figure out which function is greater?

    • @farhanrahman8327
      @farhanrahman8327 9 ปีที่แล้ว +9

      Amith Valentine Set the functions equal to each other and find their intersecting points. Then plug in the x-values for each functions and you'll know which is greater depending on the y values.

    • @angelsweet9611
      @angelsweet9611 9 ปีที่แล้ว

      Farhan Wasee acurate

    • @physicsfun2158
      @physicsfun2158 7 ปีที่แล้ว

      make a new function (say h(x)) as difference of the two given functions(say f(x)-g(x)=h(x)) and find sign of the new function(h(x)) to get which of f(x) and g(x) is greater

  • @MrBlash93
    @MrBlash93 11 ปีที่แล้ว

    Thx u

  • @Kenlauderdale123
    @Kenlauderdale123 6 ปีที่แล้ว

    Is it okay if I draw it like f(x) and then rotate it by 90 degrees and call it f(y)?

  • @juliakim8226
    @juliakim8226 6 ปีที่แล้ว

    What is the difference between x=f(y) and f^-1(y)=x?

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว +1

    now there are comments : )

  • @shahadas907
    @shahadas907 6 ปีที่แล้ว

    you are amazing

  • @wololo10
    @wololo10 14 ปีที่แล้ว

    very nice

  • @Incognito-uw3jk
    @Incognito-uw3jk 9 ปีที่แล้ว +1

    I'm confused how you got the intersection points of 1 and -1 by setting it equal to 0?

    • @sevranararis7704
      @sevranararis7704 9 ปีที่แล้ว +1

      +Diamond Hardman That's exactly right. Plugging in either of those numbers will both equal to Zero.

    • @vietnamcustomersuccess
      @vietnamcustomersuccess 9 ปีที่แล้ว +1

      +Diamond Hardman you have to set each piece = to 0 that will give you. y = 0, y - 1 = 0, and y + 1 = 0. For the second and third equation you would add and 1 to the second equation and subtract 1 from the third equation. Thus, you get +1 and -1.

  • @ziramrivera
    @ziramrivera 12 ปีที่แล้ว

    uhm. Does your technique only work on functions with respect to y (right mots func minus the left most func) ? please give me an answer 'coz we're doing it with respect to x.

  • @MzVixen05
    @MzVixen05 13 ปีที่แล้ว

    Need a 70% for finals on Thursday... hopefully this will do the trick? *fingers crossed some angels start singing after watching this* ('',)

    • @jensmalzer6344
      @jensmalzer6344 3 ปีที่แล้ว

      Did you pass?

    • @MzVixen05
      @MzVixen05 3 ปีที่แล้ว +2

      @@jensmalzer6344 I did! I went on to do an Honours degree and even finished top of my class. Oh how this seemingly little video helped me :D

  • @TJC360X
    @TJC360X 10 ปีที่แล้ว

    Thanks. God Bless you

  • @axpence
    @axpence 12 ปีที่แล้ว

    Thanks for the videos, with Khan academy you can speed up the video if you have HTML5, How come I can't do that for any of your videos @PatrickJMT
    ?
    Thanks
    Alex

  • @salwarafi9812
    @salwarafi9812 7 ปีที่แล้ว

    why is the point of intersection +1 and -1 ???

  • @smocloud
    @smocloud 5 ปีที่แล้ว

    I’m only here because I have a problem that is extremely easy to solve with integration with respect to x, but it requires me to do it also with respect to y, and what’s killing me is I can’t, for the life of me, get the same answers. They should logically be the same since it’s a measure of area, but my area with respect to y is larger by 5.

  • @errolgonzaga3751
    @errolgonzaga3751 12 ปีที่แล้ว

    i dont get how you make the graph. what is the connection of 1/2 in that? 5:18

  • @sultanayeasmin3444
    @sultanayeasmin3444 7 ปีที่แล้ว

    When we'll use integration with respect to x or y?? I can not understand.

  • @juanvolvoturbo
    @juanvolvoturbo 8 ปีที่แล้ว

    I think the left most point in the function y^3-y would be sqrt(1/3) not -1.

  • @JosSerrano11
    @JosSerrano11 13 ปีที่แล้ว

    tahnks thanks thanks!!!!!!!

  • @sebastianmartinez7963
    @sebastianmartinez7963 5 ปีที่แล้ว

    is the answer 8/5?

  • @starscream7755
    @starscream7755 11 ปีที่แล้ว

    you rock

  • @madbulgarian6020
    @madbulgarian6020 9 ปีที่แล้ว

    I had a pen no function lmfao that made my day!

  • @TimPL
    @TimPL 16 ปีที่แล้ว

    Cool, thx:)

  • @skyfaze
    @skyfaze 15 ปีที่แล้ว

    thanks my nagga !!!!!!!!

  • @Scarabola
    @Scarabola 5 ปีที่แล้ว +1

    x=g(y) fails the vertical line test

  • @BubbleCatFTW
    @BubbleCatFTW 9 ปีที่แล้ว +2

    im confused when you do it with respect to x and respect to y

    • @Jay-mp3wv
      @Jay-mp3wv 9 ปีที่แล้ว +1

      +BubbleCatFTW You just have to examine your graph and figure out which one is easier to do.

  • @telodadar
    @telodadar 16 ปีที่แล้ว

    why is there no comment?? i like this vid~

  • @mccauleybacalla2228
    @mccauleybacalla2228 ปีที่แล้ว

    i find it confusing since we dont have this lesson (YET)

  • @ArthurSperotto
    @ArthurSperotto 9 ปีที่แล้ว

    THANK YOU!!!!

  • @ProjectORION89
    @ProjectORION89 12 ปีที่แล้ว

    ...and it isn't just me either... the other vids work fine.

  • @muaaz19
    @muaaz19 6 ปีที่แล้ว

    His pen had a malFUNCTION ... lol

  • @mamu7mich
    @mamu7mich 11 ปีที่แล้ว

    lol right most function, left most function and pen malfunction. :p

  • @angelstephani982
    @angelstephani982 12 ปีที่แล้ว

    you are smarter than the integralcalc krista

  • @SuperfryGaming
    @SuperfryGaming 12 ปีที่แล้ว

    Lol, Had a pen malfunction

  • @movalex9713
    @movalex9713 4 ปีที่แล้ว

    I dont like the fact that he is left handed

  • @rishujeetrai5780
    @rishujeetrai5780 5 ปีที่แล้ว

    Wtf

  • @ProjectORION89
    @ProjectORION89 12 ปีที่แล้ว

    Sound on this is messed up... barely audible.

  • @miranuzeri979
    @miranuzeri979 8 ปีที่แล้ว +1

    more like how to draw graphs 😒

  • @jensmalzer6344
    @jensmalzer6344 3 ปีที่แล้ว

    WHATS THE POINT OF MAKING A VIDEO IF U ARENT EVEN GONNA SOLVE IT???

  • @ActuallyAudacity
    @ActuallyAudacity 7 ปีที่แล้ว

    I never respect it. Y, you ask?