Introduction to trigonometric substitution

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  • Опубліковано 17 гру 2024

КОМЕНТАРІ • 85

  • @jasonjackson4555
    @jasonjackson4555 3 роки тому +44

    OMG. I remember this from undergrad years ago. I’m glad this is in my rear view mirror. Good luck to anyone taking integral calc now! Don’t give up!

  • @leopardduck4490
    @leopardduck4490 3 роки тому +45

    An entire lesson of calculus that went halfway over my half-asleep head, explained perfectly in under 9 minutes. Huzzah!

  • @Yh-gu3cw
    @Yh-gu3cw 7 років тому +41

    This is the best explanation of trig substitution on youtube!

  • @danielkhromov9724
    @danielkhromov9724 Рік тому +7

    You've saved my midterm. A true legend

  • @lucasargandona4658
    @lucasargandona4658 4 роки тому +13

    This is exactly what I was looking for. Thank you Sal!

  • @theodoresweger4948
    @theodoresweger4948 5 років тому +9

    Thank you now that I understand the patharoris triangle, I don't have to memorize anymore, I simply use your method from the beginning. This has made my day. Thank you will use this future..

  • @fiorellasalazar6400
    @fiorellasalazar6400 3 роки тому +3

    Best professor I've ever had right here 💰💰

  • @vladimirmiloserdov7018
    @vladimirmiloserdov7018 3 місяці тому

    Prof. was explaining this for 70 min, and I did not understand anything. The 9 min video saved my life.

  • @kooltyme
    @kooltyme 4 роки тому +13

    i knew it had to do with the pythagorean theorom and trig and stuff, but people online just kept saying "ok so basically memorize this and ye when u see this do this, when you see this do this, and when you see this do this"

    • @bubble_cookie9000
      @bubble_cookie9000 9 місяців тому

      Same bro same...
      I came to know this is supposed to be different while solving questions and asking doubts online (google and stuff) r8 before exams-

  • @23232323rdurian
    @23232323rdurian 5 років тому +34

    I was really confused for a while cuz your '4' looked like a 'u' to me......

    • @rajeng2453
      @rajeng2453 4 роки тому +2

      He says it's square root of 4 - x^2 in the beginning

    • @ahuman6546
      @ahuman6546 4 роки тому +2

      Now that u said it, I can't stop but sees 4 as u now ;-;

    • @Steffystr8mobbin
      @Steffystr8mobbin 3 роки тому +1

      Missed the beginning as well and thought it was u as well

  • @vincentgriffin9202
    @vincentgriffin9202 3 роки тому +4

    I love his voice

  • @deckearns
    @deckearns 4 роки тому +5

    This is excellent!! Thank you.

  • @SlaveofAllaah7
    @SlaveofAllaah7 2 роки тому +1

    Wow..thanku soo much..this video helped me a lot ❤️🔥

  • @gutsnutsnews3284
    @gutsnutsnews3284 9 років тому +8

    Great vid!

  • @jieyuenlee1758
    @jieyuenlee1758 Рік тому

    For me doing trigo subsitution,I will think about how to get rid of the sqrt first just like 3:06 I straight away let x=2sinø then sqrt(4-x²)=2cosø

  • @curtpiazza1688
    @curtpiazza1688 3 роки тому

    Clear and concise.... Thanx!

  • @baddack6137
    @baddack6137 5 років тому +3

    you can just do it by factorising 4 and substituing by ( x/2)

    • @newkid9807
      @newkid9807 4 роки тому

      Buzz kill

    • @erichuang5971
      @erichuang5971 4 роки тому

      That's what i was thinking two

    • @OnePieceFan4765
      @OnePieceFan4765 Рік тому

      Well yea this one was just probably picked as an easy example. I mean this is a well known integral to begin with lol integral of 1/sqrt(a^2-x^2) = arcsin(x/a)

  • @calistairene998
    @calistairene998 3 роки тому

    thank you for the explanation

  • @ludvighannebo5338
    @ludvighannebo5338 5 років тому

    Great video!

  • @diogopaivagoncalves6822
    @diogopaivagoncalves6822 2 роки тому

    Thank you bro !

  • @Ember_Lumen5
    @Ember_Lumen5 Рік тому +2

    I got an A in differential calculus and an A in integral calculus. Have fun to everyone who is doing this topic. 🤣

  • @MuksEmmaN
    @MuksEmmaN 2 роки тому +2

    Question for the first example could you not substitute x to be 2cos(theta) as well because 1-cos^2(theta) = sin^2(theta).
    Then eventually your answer will result in terms of cosines???

  • @fifa1078
    @fifa1078 9 років тому +1

    why does this only have 2000 views considering he has over 2.000.000 followers???

    • @matthewgarber5517
      @matthewgarber5517 8 років тому +5

      Dan Alexander how many people actually need help with calc 2 material. Khan academy teaches algebra 1 and even lower math I believe.

  • @foureyesue
    @foureyesue 3 роки тому

    i didn't it at the first time of seeing this but thank you for explaining

  • @araragi5577
    @araragi5577 2 роки тому

    can we solve the sinh(x) and the rest of the conditions and the inverse with the same rules? i mean is it ok or is it depletable and thanks

    • @isavenewspapers8890
      @isavenewspapers8890 6 місяців тому

      You can solve certain integrals by substituting in hyperbolic functions. Probably not this one, though.

  • @JohnSmith-yv5bn
    @JohnSmith-yv5bn 3 роки тому

    03:19 If x = 2sinΘ then dx = 2cosΘ dΘ - why?

    • @ahhh7025
      @ahhh7025 2 роки тому +1

      dx = derivative of x, derivative of sin is cos so derivative of 2sin(theta) = 2cos(theta) and a d(theta) to replace dx

    • @jeffthevomitguy1178
      @jeffthevomitguy1178 Рік тому +1

      Algebraic way of seeing it:
      x=2sin(t)
      dx/dt=2cos(t)
      dx=2cos(t)dt

  • @rem.31
    @rem.31 2 роки тому

    it's perfect

  • @cartoonscene3000
    @cartoonscene3000 3 роки тому

    Bless u

  • @paromita_ghosh
    @paromita_ghosh 2 роки тому

    Ehy this substiturion is for actue angles inly what about obtuse angles?

    • @jeffthevomitguy1178
      @jeffthevomitguy1178 Рік тому

      Every obtuse angle can be redefined as the sum of kpi/2 + some acute angle which will return the same value as the obtuse angle.

  • @vincentnguyen2558
    @vincentnguyen2558 5 років тому +1

    Why does "x" have to be on the vertical leg?

    • @flownmoon5444
      @flownmoon5444 5 років тому +1

      Vincent Nguyen does not matter

    • @TheTacticalMess
      @TheTacticalMess 4 роки тому +1

      @@flownmoon5444 I know I'm late but doesn't it kind of matter if it changes what is adjacent to theta? How I'm confused is how he chose the adjacent side to be the sqrt(a^2-x^2) as opposed to the opposite side?

    • @a_smile55
      @a_smile55 4 роки тому

      @@TheTacticalMessHave you figured it out? I could use your help

    • @jeffthevomitguy1178
      @jeffthevomitguy1178 Рік тому

      @@TheTacticalMessif u have x be the hortizonatal leg, theta will be the top angle 📐

  • @ssebuyiiraarnold261
    @ssebuyiiraarnold261 2 роки тому

    Why did you use 2 on the hypotenuse, where did you derive it

    • @jeffthevomitguy1178
      @jeffthevomitguy1178 Рік тому

      It comes from the Pythagorean theorem, c is the hypotenuse the longest side

  • @jerthalp6197
    @jerthalp6197 9 років тому

    I love math

  • @bubble_cookie9000
    @bubble_cookie9000 9 місяців тому

    I was expecting the stuff like "substitute x with tanθ" kinda questions when i searched this topic tbh-
    I didn't knew these formulas had this kinda background 👀
    If anyone knows bout what I'm rendering to, pls do name it so that i can search it up-
    Atleast within a month of this coment getting pasted (I've exam) 👀

  • @kwanelekhomo9969
    @kwanelekhomo9969 8 років тому +7

    This is shady, if you make the adjacent side be x you get some negative thingis, what is shady is that you did not explain why you made the other side be x

    • @shavuklia7731
      @shavuklia7731 8 років тому +2

      yea i did the same thing with the adjacent side and i got weird shit

    • @izreyo8997
      @izreyo8997 7 років тому +2

      tru i got -arccos(x/2) + c

    • @JDMaxton1999
      @JDMaxton1999 4 роки тому

      Yeah so this is 3 years late, but I think if you're going to make the sine sub you must do the opposite side. If you do adjacent I think you get some arccos stuff. I dunno if it's explicitly wrong, just how he solved it

    • @That_One_Guy...
      @That_One_Guy... 4 роки тому

      x would always be less than the adjacent side in this case, but if x be in the front it would be something like x^2 + c^2 and you use 1+tan^2(theta) = sec^(theta), but if you were talking about x^2 - c^2 where x is less than c, you can't use trig sub, but you need to use what's called hyperbolic sub (because if x is greater than adjacent it wouldn't be a point in the circle anymore,, hyperbolic function is another counterpart of trigonometry, they have similar name with them but you add -h to imply that it's hyperbolic function, they are : sinh(x), cosh(x),tanh(x),csch(x),sech(x),coth(x). sinh(x) is defined as (e^x - e^(-x))/2, cosh(x) = (e^x + e^(-x))/2 , the rest you should know with trigonometry definition (and try to come up with some hyperbolic identity, they are needed to solve something like integral(x^2 - c^2)). They are not made up function, you will be mind blown to know that trigonometric function and exponential function can be related by a very special number, and by using that number hyperbolic function definition with euler number can be found.

    • @veljko100able
      @veljko100able 4 роки тому

      that's what confused me also, the truth is you can do it both ways the answer will only differ by a constant -arccos(x/2) + c and arcsin(x+2) + c. If you plot those two function they will look the same

  • @blinkerhawk
    @blinkerhawk 4 роки тому +1

    why hypotenuse is 2 in the first place?

    • @ahuman6546
      @ahuman6546 4 роки тому +1

      It's because the square root of 4 is 2

  • @fuzyjustin
    @fuzyjustin 8 років тому +1

    okay vid!

  • @beucan9200
    @beucan9200 9 років тому +3

    4:46 when you say "this equals to dBETA" i thought u said debata which translates to english into "debate"

  • @yosefmehio8862
    @yosefmehio8862 2 роки тому

    How/Why did he have 2 in the Hypotenuse? Where/how did he get that?

    • @jackrain0461
      @jackrain0461 Рік тому

      From the 4 in the bottom of the original equation. Sqrt (4) = 2. Think a^2 + b^2 = c^2. Where c^2 equals 4.

  • @paromita_ghosh
    @paromita_ghosh 2 роки тому

    Sal i still couldnt see the trees for the forest lolp

  • @Wakawakamatic
    @Wakawakamatic 4 роки тому

    eerie noise at @4:48 anyone?

  • @nimratdosanjh7142
    @nimratdosanjh7142 8 років тому

    I love you.

  • @siddhantkumar6932
    @siddhantkumar6932 8 років тому

    o

  • @MagicmanFTWmc
    @MagicmanFTWmc 9 років тому +1

    First lol

  • @John-wx3zn
    @John-wx3zn 3 роки тому

    That is not a 4. that is a u. If you going to teach, don't be so sloppy. Your learners need to be able to see what you have written. Come on now.

    • @jackrain0461
      @jackrain0461 Рік тому

      In the first 8 seconds he says its a 4

  • @ShamimAhmed-wg9zd
    @ShamimAhmed-wg9zd 7 років тому

    Its not hard task..so easy math.

  • @kofibaffoe1200
    @kofibaffoe1200 8 років тому +4

    Christ is coming soon believers lets get prepared