integral of sqrt(1-4x^2) ,Trig Substitution, calculus 2 tutorial

[@Dank_SomeOne]

I love how you go through each step so that it's all so easy to understand. Thank you, and keep up the good work!

[@TimeTraveler-hk5xo]

Genius! Brilliant! Exactly what I was looking for, and much more comprehensive and understandable than most other videos/forum threads on this integral!

[@pauloborges552]

THX from Brazil !!!! love ur guides ! thx

[@josueobettcoelloperez3186]

Hola hermano . Soy mexicano y veo tus videos desde ya hace un tiempo gracias a ti pase mi materia de cálculos integral. Gracias mil gracias

[@carlosulloa133]

Como te va amigo?

[@Sachinvermafzd]

Nice video, watching from India❤❤

[@Sachinvermafzd]

Hi sir I am watching your video in India. ❤❤ Thanks sir for help solve to query questions

[@exlife9446]

√(1-4x²): x belongs to [-1/2, 1/2]，so when x = 1/2 sinθ than -1

[@mayajames2601]

these videos are honestly the best

[@blackpenredpen]

Thank you!

[@MissStuckOnBandaids]

thanks for also putting the section # and problem #! it makes the problem easy to find, this of course assuming everyone is using the same textbook! thank you!

[@nebiyathamza]

thank you !! This video is 6 years old but still very relevant in 2021.

[@rifaathanver1221]

Thanks. I love to watch your tutorials. Great job.

[@日本人じゃありません]

Found an another way to solve this question. Let x = sinycosy On differentiating both sides we get: dx = cos(2y)dy Now back to the question: ∫sqrt(1 - 4x^2)dx = ∫sqrt(1 - 4sin^2ycos^2y)•cos(2y)dy = ∫cos^2(2y)dy [After simplifying] = (1/2)∫1 + cos(4y)dy = (1/2)y + (1/8)(sin4y) = (1/2)y + (1/4)sin2y•cos2y ...(1) Now, we know that x = sinycosy Therefore, 2x = sin(2y) ...(2) After constructing a right-angled ∆, we get: cos(2y) = sqrt(1 - 4x^2) ...(3) And from equation (2), we get: y = (1/2)arcsin(2x) ...(4) Putting the values of sin(2y), cos(2y) and y from equations (2), (3) and (4) respectively to equation (1), we get: (1/2)y + (1/4)sin2y•cos2y = (1/4)arcsin(2x) + (1/2)x•sqrt(1-4x^2) Hence, ∫sqrt(1 - 4x^2)dx = (1/4)arcsin(2x) + (1/2)x•sqrt(1-4x^2) + C Thank you..

[@sabbirsaif475]

Thanks!

[@josephshaff5194]

Thanks. Just started this. Reading through.

[@briannabyrd4283]

Thank you so much for these videos! They are invaluable and you explain very well.

[@garciabaciliosergio4272]

Gracias chino, sólo vine buscando la parte del sen (2x), pero aún así se agradece lo que haces sigue así

[@ellerose12]

Thank you so much! I'm doing physics in college and never really got integration (apart from the basics) and you've really helped!

[@doublejstudio5950]

Honestly You're literally saving my life for my cal 2 course :D Keep up the good work, much love from Canada!

[@alanvincent9394]

Exactly what I was looking for. Thank you from England.

[@georgiyotov4512]

You could also substitute u=2x (, because 4x^2=(2x)^2), so that you get 1/(2sqrt(1-u^2))du, which integrated is 1/2arcsinu+C=1/2arcsin2x+C

[@Hzaxoyma]

Thank you teacher keep going

[@blubworth]

i love you so much ty

[@StephenNilsen123]

You saved me man. You are awesome!

[@mildredashley9481]

You are saving me from wringing my brain for answering this equation for my daughter. This math for me was 20 years ago

[@auditore63]

Inday Girlie your daughter should look up how to solve it herself

[@joandysuriel4582]

Thx from DR 🇩🇴🇩🇴

[@jazzfb5570]

Genio! Es un método diferente del que me enseñaron, y definitivamente me quedo con tu enseñanza. Gracias! (Genius! It's a different method than the one I was taught, and I definitely stick with your teaching. Thanks!)

[@Skaterschannel]

Thank you for having such useful videos!!

[@danielroh4543]

Thank you goat

[@gemagarcia246]

thanks for all the help i REALLY appreciate your videos!

[@fangyuju1660]

你讲的超级棒，比外国人讲的好！给你个赞哦

[@blackpenredpen]

+Fangyu Ju 謝謝~

[@kalebdean6870]

thank you so much, your explanation was really helpful

[@athulyac9271]

Thanks .. brilliant and easy to understand

[@mujdemerhamet]

thank you ^_^ ...... from Algeria

[@AnthonyCronejr]

You are a wonderful person

[@anupkumarjha5172]

What's in your hand.i saw it first time.. amazing

[@blackpenredpen]

Just a mic.

[@satrickptar6265]

Its a pokeball

[@anasofia5272]

Thank you very much, it helped a lot to solve this problem

[@symt3880]

Sir, I have the same question but with a + sign instead of a - sign. How do i do it please? Thank u

[@baronajosesek]

Use tan(x)

[@rrestapani]

Thanks from Zimbabwe

[@faisalmohamed4595]

4:44 the integral of cosx is - sin not positive sin

[@erezsolomon3838]

Wrong

[@con_el_maestro3544]

That is wrong the derivative of -sinx is -cosx NOT cosx

[@Onide452]

thanks!!!

[@nikolashadjipaschalis5629]

Hi Sir Im trying to evaluate the integral of 1/sqrt(a^2-x^2) using both cos and sin substitution. With x=sinu I get arcsin(x/a) and with cosu I get -arccos(x/a) but when i substitute values for x and a I get different results why is this? Am i doing something wrong?

[@nikolashadjipaschalis5629]

does it work for cosine substitution instead of sine?

[@JealousA-1]

is it wrong to apply the formula directly?

[@henriqueribeirohott7800]

YOU ARE MY NEW GOD

[@foxhound1008]

What if "a" is not a perfect square? Will that matter in the integration?

[@entvl]

я наверное первый словянский коментатор , но что бы я без тебя делал >

[@blackpenredpen]

google translate: "I'm probably the first Slavic commentator, but that I do without you"?

[@Mariusz-rj8ye]

The correct translation has a little different meaning (like this): but what would I do without you

[@gnus7412]

Thank u so much. it was so helpful

[@saberspeed77]

As usual, I don't understand jack, but randomly in a year, I will magically understand everything. Very weird.

[@sashacaroline267]

and if it was the Integral of sqrt(5-4x^2) or sqrt(3+4x^2)?

[@angelalealkarim2697]

JESUS FUCKING CHRIST THANK YOU SO MUCH IM UR BIGGEST FAN

[@killerammermc2540]

What if it's sqrt(4-y^2) is it the same process.. instead of x it's y

[@eliasgomes3390]

muito bom somente o resultado que deu errado e 1/4 arcoseno(2x) + 2x raiz de 1-4x^2

[@przemysawkwiatkowski2674]

Why sqrt(cos^2)=cos? Why not |cos|?

[@oscarotaloraguerrero3787]

Sos grande mostro!!

[@snipez285]

Hey sir, where did you study? your awesome btw :) im studying for A level math :)

[@blackpenredpen]

I teach here in Los Angeles

[@I3oblivion]

I'm late, but amazing explainer, thank you very much!

[@MrOLOY-mj8fi]

Thanks from senegal :D

[@uedsongaiekmendessouza9432]

Sou brasileiro e não sei o que é mais difícil integral ou aprender inglês ks

[@EduardoMoreno03]

este momento donde la clase de ingles surte efecto

[@Sonatarium]

That final final final answer!!!

[@altera1882]

Ok so sin(2∆) = 2sin∆cos∆, What about cos(2∆)? What about tan(2∆)? Anyone?? I haven't been thought this anywhere

[@williampayne2993]

Why cant we use x = cos u why do we have to use x = sin u?

[@dildobaggins2759]

It would be better if someone actually showed the triangle for this question...?

[@alexprocel91]

What if you ended with cos(2theta) instead of sin(2theta). Cos(2theta) has 3 identities..

[@blackpenredpen]

Procel91 they'll all work

[@TheHaawkZ]

very good thanks a lot

[@manzoorhussain-zn1ig]

If on the place of "a" with out how it can solve

[@rythmx123]

just let 2x = sinx 😢😢

[@AnujaAdityaVlogs]

thankyou 😿

[@melodynamics9957]

口音像华人!! where are you from?

[@blackpenredpen]

melodynamics hi, 我是來自台灣

[@melodynamics9957]

教学好好，谢谢你！I'm from malaysia!!

[@blackpenredpen]

melodynamics 謝謝收看我的視頻。

[@l.choitz6472]

that is a nifty mic

[@Joao50297]

nice!

[@NiteshKumar-fb7uv]

Good

[@0501245]

Great.

[@Hzaxoyma]

Hii 2024❤

[@gammapanda3751]

I love you.

[@blackpenredpen]

I love you too!!!

[@karraraljarah7633]

Very hard

[@Gamma_Digamma]

Hypotenuse

[@denissegrijalva1596]

idol

[@circleofthytyrants]

W

[@taskmaster5437]

All that manipulation just to figure out the anti-derivative of sqrt. 1 - 4x^2. I'm sorry, but I hate Calculus lol.