Double integrals of type I and type II regions (KristaKingMath)

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  • Опубликовано: 13 янв 2025

Комментарии • 190

  • @McCloo57
    @McCloo57 5 лет назад +27

    a 12 minute video is literally better than a 3 hour lecture. Thanks!

  • @cfaion341
    @cfaion341 8 лет назад +36

    your channel is a gold mine. donno how to thank you, seriously!

    • @kristakingmath
      @kristakingmath  8 лет назад +16

      You just did! :D I'm just happy to help, so thank you for letting me know that you're enjoying the videos!

  • @eamonbellful
    @eamonbellful 9 лет назад +23

    I pay thousands of dollars to take math courses at my university and yet I learn better and more from your videos. Not only does that show how great your videos are, it also shows a huge flaw in our education system.

    • @watchmanling
      @watchmanling 9 лет назад +7

      The sad thing is social mechanism is totally controlled by those big companies. If you want to survive, you have to find a job which means you have to have a degree, no matter how it is futile. Then your tuition for those education system support a huge amount of useless faculties who promote and brainwash generation by generation.

    • @williamkoleszar3301
      @williamkoleszar3301 5 лет назад +3

      This is why college maths education could be greatly improved if we just watched online lectures for everything and professors served as coaches/facilitators to guide conversations in class and help students with problems. In other words, students would watch lectures outside of class and inside of class would be one big group study. No more wasted hours staring a white board you don't understand.

    • @leslieglen9047
      @leslieglen9047 5 лет назад +3

      @@williamkoleszar3301 That's called the "flipped" classroom model, and many of us are using that in our classrooms. The downside is that many students DON'T watch the videos, and then our class time is spent trying to get them "caught up" and the students who DID watch and need my "coaching" help don't get it in the proportions that they should...

    • @williamkoleszar3301
      @williamkoleszar3301 5 лет назад +2

      @@leslieglen9047 That's true, there's one professor who teaches a flipped classroom at my university. Yes, we waste a lot of time catching people up. If this change will ever make a significant impact, students, parents, teachers, and the businessman making financial decisions would all have to be educated on the benefits of the "flipped" philosophy

  • @mms1064
    @mms1064 9 лет назад +109

    Thank you
    My tuition money should go to youtubers like patricjmt and integralcalc. Not my professors!

  • @hailey2822
    @hailey2822 5 лет назад +1

    BLESS YOU!!! YOU JUST SAVED MY GRADE!!! seriously, no one else explained the differences between regions as well as you did, completely changed how I view this entire section!!!

  • @davidtiah
    @davidtiah 8 лет назад +3

    I learned from you in 30 minutes what I couldnt understand from my lecturer in 5 hours. Thanks :)

  • @notSavant
    @notSavant 8 лет назад +4

    This is incredibly simplified which makes it easy to follow... thanks i love your videos, it's a shame there are some parts missing, but still, thanks!

  • @TheFarmanimalfriend
    @TheFarmanimalfriend 4 года назад +1

    I am finally getting a handle on double integrals. Your explanations are immensely helpful. Thank you.

  • @ItsThatMilkshake
    @ItsThatMilkshake 8 лет назад +1

    Krista King has done it again. Thank you

  • @webspierre9296
    @webspierre9296 9 лет назад

    Great job on helping calculus student with evaluating an interated integral and finding the area of a plane. How to use a double integral to find the volume of a solid region is another. Thank you integralCALC for the tutorial.

  • @FathimaMinna
    @FathimaMinna 9 лет назад +1

    You helped me understand the portions that I spent 4 hours on without understanding a word. Thank you so much. I can't help but feel grateful! 😁

  • @swethajeya574
    @swethajeya574 8 лет назад +5

    Thank you! my quiz is coming up soon! and this really helped me understand. College lecture notes are so confusing! thank u much! very clear!

    • @kristakingmath
      @kristakingmath  8 лет назад +1

      You're welcome, I'm so glad it helped! Good luck on your quiz, I hope it goes great!

  • @moinaction
    @moinaction 6 лет назад

    I've always found your tutorial helpful and part of it is how you go in depth explaining every steps one by one. The way you teach, I bet a kindergarten kid could follow along and do well in the exam. Thanks for all your helps and God bless.

  • @whendidyoutubeaddhandles
    @whendidyoutubeaddhandles 9 лет назад

    what my professors notes couldn't help me understand after two hours of frustration, you could within minutes. so helpful, I can't thank you enough :)

    • @kristakingmath
      @kristakingmath  9 лет назад

      +chuck norris You're welcome, I'm so glad it helped!

  • @Prodigy906
    @Prodigy906 9 лет назад +9

    Thank you for always being so clear and helpful! You explain everything so well and don't go too fast! ( : It really helps me as my Calc3 professor doesn't give us "steps" for how to approach problems only speeds through examples. anyway I really appreciate all your videos and the time it must have taken to do them all!!! ( :

    • @kristakingmath
      @kristakingmath  9 лет назад

      +Prodigy906 I'm so glad I can help! Thanks for the comment. :D

  • @oscarlykitty
    @oscarlykitty 8 лет назад +5

    This is incredibly helpful, thank you! (It's also great to see women doing educational content on RUclips, so keep it up!)

  • @dzarren
    @dzarren 10 лет назад +17

    Wait, the final answer of 1 is not actually the area of the regions. It is the volume of space below z=x^2 over the regions described.
    Just by looking, you can see that the area of the regions alone is actually 2, since we have 4 pieces that each take up half a unit of area.
    To obtain the area, you would integrate the function z=1, rather than z=x^2.

    • @lucyguerrero6253
      @lucyguerrero6253 8 лет назад +4

      Yess! Right, because there is a function inside the integrals. If it were just SSdA, then it would be the area, right?

    • @El650Jefe
      @El650Jefe 7 лет назад +2

      I don't think she's calculating the volume either because z=x^2 does not form a surface. z=x^2 is a parabola which is two dimensional therefore it can 't have a volume. So i don't know what in the world was just calculated. If anyone know let me know.

    • @omnimenge
      @omnimenge 7 лет назад +1

      El650Jefe i think z=x^2 can be a surface in which the value of z is constant for all y..

    • @omnimenge
      @omnimenge 7 лет назад

      dzarren i agree, however, with z=1 we are actually calculating a volume of constant thickness of 1 which has the same value of the 2d area..

    • @flyingsquirrel2620
      @flyingsquirrel2620 7 лет назад +1

      dzarren i agree. There isn't an area that equals 0,25. When we want to calculate the area of the triangle we should use 1 instead of x^2.

  • @priMoN6
    @priMoN6 9 лет назад +7

    You're the best. I wish you were my calc prof!!

  • @rubyiskira8939
    @rubyiskira8939 4 года назад

    Finally someone explained it properly, thank you!

  • @nathanfergot5710
    @nathanfergot5710 7 лет назад

    You did a great job on this explanation. Glad there are great teachers like you on RUclips!

  • @hassanhashemi6478
    @hassanhashemi6478 10 лет назад +15

    thanks, i was struggling with the concept.

    • @kristakingmath
      @kristakingmath  10 лет назад +1

      you're welcome, i'm so glad this helped!

  • @isaacmabitsela6864
    @isaacmabitsela6864 4 года назад

    just came accros this while am busy with my exam prep.
    you are the best krista king

    • @kristakingmath
      @kristakingmath  4 года назад

      I'm so glad it helped, Isaac! I hope the exam went great!! :D

  • @lifdaai6736
    @lifdaai6736 7 лет назад

    Thank you. Clarified the Type 1 and 2 definition very fast. Now it looks so simple

  • @jakerupert3603
    @jakerupert3603 10 лет назад +4

    This was so clear! Thank you for making these videos.

  • @mrmegahungry
    @mrmegahungry 7 лет назад +2

    I LOVE YOU KRISTAAA! you saved me

  • @syuhada9627
    @syuhada9627 6 лет назад

    You explain it better than anyone! thankyou so much!

  • @yesman6097
    @yesman6097 9 лет назад

    Your videos are all exceptional. You are a greater aid to my studies than my professor.

    • @kristakingmath
      @kristakingmath  9 лет назад

      +Emilian Kachev Aw thanks! Glad you like them.

  • @MikeRichards91
    @MikeRichards91 9 лет назад

    ur videos have actually saved my life keep it up

  • @nickvalencia147
    @nickvalencia147 2 года назад

    my teacher blazed over type 1 and 2 regions and i jusdt guessed what they meant all semester. no idea it was this simple, thanks

  • @jacquelinezuniga3165
    @jacquelinezuniga3165 9 лет назад

    You're so great at explaining concepts, thank you smart woman!

    • @kristakingmath
      @kristakingmath  9 лет назад

      Jacqueline Zuniga You're welcome, I'm so glad it helped!!

  • @Bluemonkey123
    @Bluemonkey123 7 лет назад

    You explain everything so well!! Way better than my prof!!

  • @raptormonkey253
    @raptormonkey253 7 лет назад +2

    thanks for making this video, everything was explained really well.

  • @ArchIVEDCinema
    @ArchIVEDCinema 6 лет назад

    These videos are really helping me get through college! Thank you so much!

  • @harshitgupta2872
    @harshitgupta2872 7 лет назад +2

    to find the area of given region(4*D1) ,we just put the lower and upper bound for dy is from -x+1 to 1and for dx 0 to 1,it gives the area of region then why we put x^2 inside double integration ,isn't it like f(x,y) which give volume by applying double integration,I just want to ask what x^2 signified becoz it is not present /use anywhere in given figured

  • @Lonewolf-vd3yn
    @Lonewolf-vd3yn 3 года назад

    Thank you! I never understood how to define superior and inferior limits when regions are II-type until I saw this video

  • @Anna-qp1fi
    @Anna-qp1fi 3 года назад

    Excellent video, thanks for putting the time in to teach us :)

    • @kristakingmath
      @kristakingmath  3 года назад +1

      My pleasure, Anna! I'm happy to help! :)

  • @aliabdu6322
    @aliabdu6322 10 лет назад +1

    Perfect , Thank you ... x^2 that's the main equation for the entire region( z=x^2) look at the first of the problem

  • @gene546
    @gene546 8 лет назад

    6:50, excuse me, ins't a right triangle what you're dealing with? I mean, you can use Pythagoras theorem to get the larger side right? Could you pleas explain

  • @BrandonOsborn404
    @BrandonOsborn404 9 лет назад

    Concise and helpful, as always - Thank You!

  • @vychuck
    @vychuck 2 года назад

    Krista Queen of Maths

  • @akashi4470
    @akashi4470 2 года назад

    Uraaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa yeeeeeeeeeeeeeeess Finally the most simple and clear explaining THANK YOU SISTER YOU ARE THE BEST

  • @joliettraveler
    @joliettraveler 9 лет назад

    Great help in understanding this concept. I can't thank you enough.

    • @kristakingmath
      @kristakingmath  9 лет назад

      +joliettraveler You're welcome, I'm so glad it helped!

  • @aznangggieee
    @aznangggieee 7 лет назад

    Thank you so much for a very clear understanding! Way better than how my professor explains it :)

  • @brij1728
    @brij1728 8 лет назад +2

    thank you mam, you cleared my doubt.

  • @amalya94
    @amalya94 8 лет назад +3

    hi! i need help! I don't understand how you get the diamond figure D1, D2, D3, D4 from the given f(x). What if Im given a curve and a line how do I start?

  • @guyyifrah849
    @guyyifrah849 9 лет назад +1

    very clear video! Thank you!

  • @HamzaM7891
    @HamzaM7891 9 лет назад +4

    Amazing! Life saver!

  • @KoolViking3
    @KoolViking3 8 лет назад

    This video helped me so much - thanks!

    • @kristakingmath
      @kristakingmath  8 лет назад

      +KoolViking3 You're welcome, I'm so glad it helped!

  • @muhammadmohsin5194
    @muhammadmohsin5194 8 лет назад +2

    You're the star

  • @lucyguerrero6253
    @lucyguerrero6253 8 лет назад +1

    Hi! Your channel is super cool! Question, though. When you do the double integrals with x^2 inside, wouldn't you get a volume, though? Thing is, I'm using this for Probability and Statistics; what goes inside the double integral is the probability function, and when you do the double integral you don't find the area of the region but rather the probability, which is the volume of some solid defined directly above the defined region. Is this right?

  • @rudzaninndwa6611
    @rudzaninndwa6611 4 года назад

    thank you so so much. this is so helpful, I understood everything.

    • @kristakingmath
      @kristakingmath  3 года назад

      Oh good! I'm so glad it all made sense! :D

  • @indian_scouser_ynwa
    @indian_scouser_ynwa 7 лет назад +1

    finally understood .thank u very much

  • @camf8646
    @camf8646 10 лет назад

    @dzarren
    To obtain the area of all four segments, I think you'd actually integrate z=1, and then take the absolute value of z=-1, and then add them together. Integrating only z=1 would give you the area of the segments D1-D4 between z=1 and the x-axis (1); integrating z=-1 from x=-1 to x=1 would give you the area of the segments D1-D4 between z=-1 and the x-axis.
    Similarly, I think you'd only take D1 and D3 into account finding the area below x^2, since x^2 never has values below the x-axis and therefore you couldn't find the area between the values of x^2 below the x-axis and the x-axis.

  • @Mo_093
    @Mo_093 10 лет назад +3

    Thanx so much.......That was really helpful !!

  • @Iwantblueberry
    @Iwantblueberry 9 лет назад +3

    I think you might have just saved my semester....

  • @JeanDAVID
    @JeanDAVID 11 лет назад +1

    I wonder why the area D1 = 1/4 ? is it not equal to 1/2 ?

  • @MakroMat
    @MakroMat 6 лет назад

    Krista hi
    I am math teacher in turkey and i am preparing math videos as you.
    Which program do you use for your videos? Can you say if you want please thanks

  • @harryrichard7106
    @harryrichard7106 9 лет назад

    whoa that was amazing. You just saved my semester... thnx

  • @awsahmed6484
    @awsahmed6484 8 лет назад

    you r a source of happiness!

  • @EngGear
    @EngGear 8 лет назад +2

    thanks a lot, I'm grateful.

  • @SarahZeineldeen
    @SarahZeineldeen 5 лет назад

    thanks alot! That sure cleared my misconceptions .

  • @younseoryu9542
    @younseoryu9542 6 лет назад

    Yeah. You are for sure x100 better than my professor who has a phd degree from Stanford

  • @1495978707
    @1495978707 10 лет назад +1

    So, where does the x^2 come from? I know it's a given, but how do they find it?

  • @nawresalkhaffaf9257
    @nawresalkhaffaf9257 8 лет назад +1

    i know that the area of a triangle is half X base X height....the height and base equals 1 so we should get the are equal 1/2..... and the are of the 4 regions shoulb be equal to 2 not 1 ............am i wright or what ?

  • @EDUARDO12348
    @EDUARDO12348 7 лет назад

    Am a bit confused regarding the orientations of integrations, I thought we integrate vertically for dy not horizontally.

  • @1972hattrick
    @1972hattrick 11 лет назад

    Intuitively I would've looked at the simple form before performing calculus. A 2x2 square with a sqrt(2)xsqrt(2) square inside leaving me with an area of 2. I'm guessing you should've taken the double integral of 3/2 x^2 rather than x^2.

  • @TheCommander454
    @TheCommander454 9 лет назад +1

    Thank u so much that's really helpful .

  • @naveenvarma3359
    @naveenvarma3359 9 лет назад

    thank you for the video,it helped me a lot

  • @leostrauss549
    @leostrauss549 11 лет назад

    Just curious, but you wouldn't happen to know about complex variables and calculus in the complex plane? Like contour integrals and residue theorem. I'm taking that course in the fall semester. Thanks anyways. Peace out!

  • @moshibudikgaogelo9383
    @moshibudikgaogelo9383 4 года назад

    thank you so much. this was really helpful

    • @kristakingmath
      @kristakingmath  4 года назад +1

      You're welcome, Moshibudi! Glad it was helpful! :)

  • @Siggfuggggg2000
    @Siggfuggggg2000 6 лет назад

    I don't understand why you put in the x^2 in the double integral after describing the triangular region

  • @watchmanling
    @watchmanling 9 лет назад

    Hi I can't identify the type for this area between a unit circle center at origin and another function y>x . Can you advise? Thank you so much.

  • @TheHenkOwNzz
    @TheHenkOwNzz 4 года назад +1

    How can a triangle (D1) that is half the area of a 1x1 square be 1/4 instead of 1/2?

    • @VK-sp4gv
      @VK-sp4gv 3 года назад

      I have the same question, like many others in the comments. I think the value of 1 she found is the volume under the surface z=x^2, not the total area of the four trangles, which 2.

  • @peiyingwu3036
    @peiyingwu3036 8 лет назад +2

    very helpful

  • @ottoomen5076
    @ottoomen5076 7 лет назад

    Could someone explain how the x^2 relates to the problem. I realize if you substitute x^2 with one you get the area of the triangle. What is the purpose of x^2? formulas like x^2 are given in my textbook but the connection between x^2 and the area of the triangle is never explained.

  • @GH123XL
    @GH123XL 11 лет назад

    Also, do u have a video on triple integral?

  • @GH123XL
    @GH123XL 11 лет назад

    Hi Krista, I wonder if you only concentrate on integral only and not cover topics such as tensor calculus. Thank you very much.

  • @kristakingmath
    @kristakingmath  11 лет назад +2

    No, but maybe I had an extra cup of coffee that day. :)

  • @ethanszuba606
    @ethanszuba606 3 года назад

    💯saved my grade

  • @saqib3s
    @saqib3s 4 года назад

    Thanks Krista

  • @sudindras.8952
    @sudindras.8952 8 лет назад

    krista thanks. the explanation is done very well. But area of a triangle is A=0.5*b*h, and in case of D1 its 1/2 not 1/4 can you justify please.

  • @shane2678
    @shane2678 6 лет назад +1

    You are the woman of my dreams. Beautiful & awesome at maths! ;) Anyway, creepiness aside, thank you for the video. It was really helpful. I understand double integration - particularly how limits of integration are worked out - much better after watching it. :D

  • @Littlejonjontheking
    @Littlejonjontheking 9 лет назад

    So the difference between type I and Type II is whether you are looking at the graph from x or y.

  • @johnvolpi125
    @johnvolpi125 3 года назад

    Hi Krista King. I tend to learn a lot from your videos, but part of this video confused me. I thought 1/4 would be the volume between z = 0 and z = x^2 in D1, but you said 1/4 is the area of D1? I thought the area of D1 would be 1/2. I got 1/2 by having 1 instead of x^2 inside the integrals. Am I missing something? Thank you.

  • @CreativeCat333
    @CreativeCat333 7 лет назад +3

    I'm in love with your voice. 😍

  • @Blacktop_Battle
    @Blacktop_Battle 4 года назад

    But shouldn't the area of all the triangles amount to 2? since the square is 2x2 (area of 4) and the triangles take up half of the square???

  • @anthonykallingal4263
    @anthonykallingal4263 7 лет назад

    Thank You, however when I am finding D1 using Type 2, I get answer as 5/12 instead of 1/4. Not sure where I am going wrong.

  • @shehrozafzal9208
    @shehrozafzal9208 8 лет назад +2

    you are amazing........!!!!!!!!!

  • @sultnot2
    @sultnot2 9 лет назад

    always perfect!

  • @victorserras
    @victorserras 6 лет назад

    Why use double integrals to calculate area in the first place? And you drew a 1 by 1 square and divided it in half, so shouldn't the area of the triangle be 1/2?

  • @zackgrey4472
    @zackgrey4472 3 года назад

    You're my new calculus professor lol. Mantel being passed down from The Organic Chemistry Tutor, and that's how you knowwww you're good!!! Haha

  • @FaelFabriEngineering
    @FaelFabriEngineering 9 лет назад +1

    I finally got it

  • @strugglingcollegestudent
    @strugglingcollegestudent 2 года назад

    Thank you so much!

  • @chaimaedoudou1699
    @chaimaedoudou1699 5 лет назад

    Will you please do some exams you explanation is wonderful

  • @LadyBioshock
    @LadyBioshock 9 лет назад

    Could someone please tell me the program they used to make these? I really need to know!

    • @kristakingmath
      @kristakingmath  9 лет назад

      +LadyBioshock I explain here: www.kristakingmath.com/my-videos Hope that helps!

    • @valecampos8999
      @valecampos8999 9 лет назад

      +CalculusExpert.com Thank you so much!

  • @abdulbasitimtiaz
    @abdulbasitimtiaz 5 лет назад

    How you get -x+1

  • @joyanz114
    @joyanz114 4 года назад

    You are amazing thank u so much

  • @maxwonkyi2546
    @maxwonkyi2546 4 года назад

    Thank you very much. I now understand😪😪

    • @kristakingmath
      @kristakingmath  4 года назад +1

      You're welcome, Max, I'm so glad it helped! 😊

  • @leader9047
    @leader9047 5 лет назад

    What is edition of calculus?

  • @mohammedshaarif4748
    @mohammedshaarif4748 6 лет назад +1

    Which software You Are using to make these videos