Integral of (x^3)*sqrt(1-x^2) (substitution)

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Integral of (x^3)*sqrt(1-x^2) - How to integrate it step by step using the substitution method!

🚶 𝐒𝐭𝐞𝐩𝐬
00:00 Rewrite expression
00:10 Substitution: u=1-x^2
00:16 Differentiate in both sides
00:28 Substitute 1-x^2, x^2 and x*dx
01:00 Rewrite expression
01:27 Integrate u^(1/2) and u^(3/2)
01:45 Simplify expression
02:06 Rewrite expression
02:27 Undo substitution: u in terms of x
02:49 Simplify expression
03:18 Add integration constant +C
03:28 Final answer!

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𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝𝐬 𝐩𝐥𝐚𝐲𝐥𝐢𝐬𝐭
► Integration by parts

► Integration by substitution

► Integration by trig substitution

► Integration by Weierstrass substitution

► Integration by partial fraction decomposition

𝐅𝐨𝐥𝐥𝐨𝐰 𝐈𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬 𝐅𝐨𝐫𝐘𝐨𝐮

𝐃𝐨𝐧𝐚𝐭𝐞

#integralsforyou #integrals #integrationbysubstitution

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🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥? 𝐅𝐢𝐧𝐝 𝐢𝐭 𝐰𝐢𝐭𝐡 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥 𝐬𝐞𝐚𝐫𝐜𝐡𝐞𝐫:

🎓 𝐇𝐚𝐯𝐞 𝐲𝐨𝐮 𝐣𝐮𝐬𝐭 𝐥𝐞𝐚𝐫𝐧𝐞𝐝 𝐚𝐧 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐭𝐢𝐨𝐧 𝐦𝐞𝐭𝐡𝐨𝐝? 𝐅𝐢𝐧𝐝 𝐞𝐚𝐬𝐲, 𝐦𝐞𝐝𝐢𝐮𝐦 𝐚𝐧𝐝 𝐡𝐢𝐠𝐡 𝐥𝐞𝐯𝐞𝐥 𝐞𝐱𝐚𝐦𝐩𝐥𝐞𝐬 𝐡𝐞𝐫𝐞:

👋 𝐅𝐨𝐥𝐥𝐨𝐰 @𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥𝐬𝐟𝐨𝐫𝐲𝐨𝐮 𝐟𝐨𝐫 𝐚 𝐝𝐚𝐢𝐥𝐲 𝐢𝐧𝐭𝐞𝐠𝐫𝐚𝐥! 😉

IntegralsForYou

This is a nice warmup in the morning :)

alberteinstein

It will save you a lot of steps if you define u=sqrt(1-x^2) for the substitution. In this case, it only needs to deal with whole integer powers.

MathSolvingChannel

bruv idk who you are, but this 3 minute video explained substitution method to me better than my high school and uni teachers, thanks a bunch :)

nejijafarli

why u^3/2 (5 ) ? i dont get this 5 / 2:33 part

jean

Thank you for this integration, please do for 1/(ax^2+b)^2

baaqarnaqi

Im watching integrals videos for fun? Im watching integrals videos for fun

fatoumatasylla

Great video! Solving integrals is allways fun!

silentmath

Plz sir try to keep some distance it can't seen clearly becoz your hand other all calculations are good

vandanaUnde

The definite integral of this function ranging from 0 to 1, according to the result of the video, it resets to both 1 and 0, how would it look?

lianohonorato

Yo quisiera saber cómo se hace esta integral, pero por sustitución trigonometrica

alejandrodavila

Interesante esta integral, me tocó una parecida en un examen y me equivoque en un paso, 😕pero viendo tus videos, he aprendido mucho, Gracias 🙌👅👌📝. ( ꈍᴗꈍ)(◠‿・)

Melek_OK.

what is the solve of this integration :
S X(√X³+4)dx

sadsagain

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