Integral of sqrt(1-x^2) (substitution + trigonometric identities)

✍🏼 integralsforyo... - Integral of sqrt(1-x^2) - How to integrate it step by step using integration by substitution!
🔧 𝐔𝐬𝐞𝐟𝐮𝐥 𝐯𝐢𝐝𝐞𝐨s
sin(arccos(x)) = • sin(arccos(x))
cos(arcsin(x)) = • cos(arcsin(x))
✅ 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞 𝐭𝐨 𝐜𝐡𝐞𝐜𝐤 𝐭𝐡𝐞 𝐬𝐨𝐥𝐮𝐭𝐢𝐨𝐧
Derivative of (1/2)(arcsin(x) + x*sqrt(1-x^2)) = • Derivative of (1/2)(ar...
🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:
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[@IntegralsForYou]

🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫: ► Integral searcher 👉integralsforyou.com/integral-searcher 🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞: ► Integration by parts 👉integralsforyou.com/integration-methods/integration-by-parts ► Integration by substitution 👉integralsforyou.com/integration-methods/integration-by-substitution ► Integration by trig substitution 👉integralsforyou.com/integration-methods/integration-by-trig-substitution ► Integration by Weierstrass substitution 👉integralsforyou.com/integration-methods/integration-by-weierstrass-substitution ► Integration by partial fraction decomposition 👉integralsforyou.com/integration-methods/integration-by-partial-fraction-decomposition 👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉 📸 instagram.com/integralsforyou/

[@AyooTube]

2:22 You re lacking a 1/2 multiplying the sin(u) (besides the one outside of the parentheses)

[@IntegralsForYou]

Hi, Ayoo Tube, you're right, I forgot to write it, but in 2:37 I realize it and wrote it ;-D

[@lorenzoortiz8966]

you know dude?? i kinda enjoy a little conversation with my math. makes me feel spooned

[@wallflower5672]

Thanks a lot for this.....

[@IntegralsForYou]

My pleasure! 😊

[@KimSeokjinnie-bs5sh]

Is it wrong if i Pose x=cos(u)???🛑

[@IntegralsForYou]

Hi! No, it is not wrong! Your answer will have arccos(x) instead of arcsin(x) since both derivatives are the same except for a constant: Derivative of arccos(x) = -1/sqrt(1-x^2) = -(1/sqrt(1-x^2)) = -Derivative of arcsin(x) Integral of sqrt(1-x^2) dx = Substitution: x = cos(u) ==> 1-x^2 = 1-cos^2(u) = sin^2(u) dx = -sin(u)du Integral of sqrt(sin^2(u)) -sin(u)du = = - Integral of sin(u)*sin(u) du = = - Integral of sin^2(u) du = sin^2(u) = (1/2)(1-cos(2u)) = - Integral of (1/2)(1-cos(2u)) du = = (-1/2)*Integral of (1 - cos(2u)) du = = (-1/2)*[ Integral of 1 du - Integral of cos(2u) du ] = = (-1/2)*[ u - (1/2)sin(2u) ] = sin(2u) = 2sin(u)cos(u) = (-1/2)*[ u - (1/2)2sin(u)cos(u) ] = = (-1/2)*[ u - sin(u)cos(u) ] = sin(arccos(x)) = kzbin.info/www/bejne/b4u0q3qum5itnpY = sqrt(1-x^2) = (-1/2)*[ arccos(x) - sin(arccos(x))cos(arccos(x)) ] = = (-1/2)*[ arccos(x) - sqrt(1-x^2)*x ] = = (1/2)*[ -arccos(x) + x*sqrt(1-x^2) ] + C Hope it helped! 💪

[@KimSeokjinnie-bs5sh]

@@IntegralsForYou omg thank you so much 💖 yeah it's really helpful ☺️iam so grateful that you answered me accurately and in a short time 🙂‍↕️✨

[@IntegralsForYou]

@@KimSeokjinnie-bs5sh It is my pleasure! ❤ If you subscribe to this channel and to the new one about derivatives it would be a huge help! Thank you! www.youtube.com/@DerivativesForYou ❤

[@KimSeokjinnie-bs5sh]

@@IntegralsForYou💖 iam already a subscriber for this channel hhh And of course I will support your new channel 🩷 you deserve it

[@IntegralsForYou]

@@KimSeokjinnie-bs5sh Thank you very much! ❤

[@giftadiawa1887]

how did we get to arcsin in number 3?

[@IntegralsForYou]

Hi Gift Adiawa! You can consider the first expression x=sin(u) and apply arcsin on both sides: x=sin(u) arcsin(x)=arcsin(sin(u)) arcsin(x)=u

[@christophsilva6816]

mais um inscrito

[@IntegralsForYou]

Obrigado! 💪

[@daniellenel7118]

HOW DOES THIS VIDEO NOT HAVE ANY SOUND?!?!?!?!?

[@dan55800]

It is not needed.

[@erinmeyers-t9w]

tank!!

[@IntegralsForYou]

You're welcome! 😉

[@kaoutharmaarafi4962]

thankss

[@IntegralsForYou]

:-D

[@nuryohan1511]

Writing too small

[@paulagabrielarojasmontejo5374]

Thank you so much. This channel is great.

[@IntegralsForYou]

Thank you! I am very proud of my channel, and I am prouder of it every time I read comments like yours! 😊

[@陈佳铭-g7y]

thank you!!!! this channel is so underrated!!!

[@IntegralsForYou]

Thank you very much! ;-D

[@jagdishtiwari9254]

Can I get a solution of underoot 1-x^3

[@IntegralsForYou]

Hi! I'm sorry but I think it is a non-elementary integral...

[@lalgerielibre9519]

Best integration channel ever

[@IntegralsForYou]

Thank you very much! 😊😊

[@googoo8462]

How come i see inconsistencies?

[@antoinesicot3879]

Sqrt(cos(u)^2) is not always equal to cos(u)

[@IntegralsForYou]

Hello Antoine Sicot, you will find a good explanation in this link: math.stackexchange.com/questions/1118400/trig-substitution-why-can-we-ignore-the-absolute-value

[@weamt8562]

Et si on a les bornes de notre intégrale de 0 à 2

[@IntegralsForYou]

Le domaine de sqrt(1-x^2) est [-1,1]: Intégrale de sqrt(1-x^2) dx de 0 à 2 = = Intégrale de sqrt(1-x^2) dx de 0 à 1 = = (1/2)(arcsin(1)+1*sqrt(1-1^2)) - (1/2)(arcsin(0)+0*sqrt(1-0^2)) = = (1/2)(pi/2+1*sqrt(0)) - (1/2)(0+0*sqrt(1)) = = (1/2)(pi/2) - (1/2)(0) = = pi/4

[@weamt8562]

@@IntegralsForYou thank you so much 😊😊

[@IntegralsForYou]

@wéã MT Avec plaisir! 😉