U-substitution With Definite Integrals

This calculus video explains how to evaluate definite integrals using u-substitution. It explains how to perform a change of variables and adjust the limits of integration - upper and lower limits.
Antiderivatives: • Antiderivatives
Fundamental Theorem - Part 1:
• Fundamental Theorem of...
Fundamental Theorem - Part 2:
• Fundamental Theorem of...
Net Change Theorem:
• Net Change Theorem - C...
Mean Value Theorem - Integrals:
• Mean Value Theorem For...
________________________________
Average Value of a Function:
• Average Value of a Fun...
U-Substitution - Indefinite Integrals:
• How To Integrate Using...
U-Substitution - Definite Integrals:
• U-substitution With De...
1st Order Differential Equations:
• Separable First Order ...
Initial Value Problem:
• Initial Value Problem
________________________________
Area Between Two Curves:
• Area Between Two Curves
Disk and Washer Method:
• Disk & Washer Method -...
Volume By The Shell Method:
• Shell Method - Volume ...
Volume By Cross Sections:
• Volumes Using Cross Se...
Arc Length Calculus Problems:
• Arc Length Calculus Pr...
__________________________________
Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/eWjRpn2Zf9ecja8 Final Exams and Video Playlists: www.video-tutor.net/

[@genevievemenz5906]

Thank you so much for not skipping steps. You're a sanity hero.

[@mogethecurator3232]

Idk what you mean, there are quite a few things I didn't get. like u cubed. Where did that come from? The bad thing about catching up on math is that on top of keeping up with new information, you have to remember every minute detail of what you've learned in the past or be destined to be hopelessly lost Edit: Which isn't the case in nearly any other subject. Even with science, concepts that don't strictly rely on math are more malleable than this.

[@capri2673]

@@mogethecurator3232 When you integrate, you add 1 to the power and divide by the same number. That's where he got the ^3 from.

[@mogethecurator3232]

@@capri2673 Ok, thanks

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[@Syntaxxed]

@@mogethecurator3232 it very much is the case in most sciences though. In chemistry for example it all builds up. It helps to just review your basic math even when you're doing 'higher' math. Good luck!

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[@ultimatekenz]

your calc homework will NOT be this easy using the same concept. you'll see.

[@bernardoramirez1759]

@@ultimatekenzstill works great as an introduction to the topic, don’t be so cocky

[@deserttan37]

@@ultimatekenzok, but the concept applies to most applications even as they get more complicated. my calc professor couldn’t teach this lesson even close to as clearly as he does. cocky little calculus baby you are huh 😂

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[@eduardo0796]

Great explanation, although I thought your lower limit could not be a bigger number than the higher limit. Shouldn't we multiply the whole integral by -1 so we can switch them up?

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[@bonelesspizza6311]

How do you know when to use u substitution vs integration by parts? When I saw the first example, I thought of by parts but he used U substitution instead. So how do we know when?

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[@ismaelersoz]

9.10 u should be 1+x^2 but it seems you missed 1

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[@jayjoy]

Thanks man I forgot I need to change limit too

[@keyb]

So I think it works with a simple set of "steps" to follow from what I could gather. 1. Use U substitution to simplify, along with finding the derivative of u. 2. Get rid of all remaining x-terms. 3. Find the lower and then upper bounds of the function. 4. Integrate u along those bounds by using part 2 of calculus. 5. Solve and you should have an answer?

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[@ItsmePrinceShalan]

What is the difference between integration by parts with this U- Substitution Rule

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[@Lomokkoe]

I feel like an idiot. I remembered the adjusting values but I didn’t pay enough attention to remember to leave u. I just would but u back in and use the original values lol

[@yaweli2968]

You can substitute back your x’x in place of uus and leave the limits unchanged.

[@jtdillon6483]

do you not need to plug in what you made u at some point?

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If there isn't something to simplify the fraction, what should I do?

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When can i use it,how do i know that i have to use it in specific problems?

[@Einfach_Ben]

Can you make a video about that but the derivative is not given, like Integral sqrt(1+4x²). I need that, plz :D

[@isaiah7141]

for the question at 5:44 is there not another negative sign added to the front of the equation since its from the bigger number to the smaller number?

[@sarahc.7386]

exactly, that’s what i thought!

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[@LuzHernandez-io6ul]

Do you have a video of U-Substition with Indefinite Integrals?

[@TheOrganicChemistryTutor]

Yep: kzbin.info/www/bejne/qZW8laGmjtNgZ9E

[@klentjosephrojo2434]

Ty

[@mionmilla7300]

I'm confused when I used the formula here got results different from the mathway calculator results. I don't know which lne is tru but I definitely followed this one here when I was solving

[@mogethecurator3232]

I'm lost at 1:58. Where did u cubed come from? There is no cubed earlier in the problem, it just seems like it comes from absolutely nowhere