U-substitution With Definite Integrals
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- Опубликовано: 21 авг 2024
- 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...
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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
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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...
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Thank you so much for not skipping steps. You're a sanity hero.
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.
@Capri Ok, thanks
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@@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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your calc homework will NOT be this easy using the same concept. you'll see.
@@ultimatekenzstill works great as an introduction to the topic, don’t be so cocky
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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?
Yes we should
The 2nd one right? The comments always save me when I think I might have done something wrong 😊
Is it the same answer either way? I just wanna confirm that
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9.10 u should be 1+x^2 but it seems you missed 1
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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?
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
You can substitute back your x’x in place of uus and leave the limits unchanged.
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Professor Organic Chemistry Tutor, thank you for solving Definite Integrals using U-substitutions in Calculus. This is the beginning of Integration Techniques in Calculus and Applied Science. This is an error free video/lecture on RUclips TV with the Organic Chemistry Tutor.
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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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hello guys, tomorrow is my final exam of calculus 3. YES I'm here watching a video on how to solve a definite integral by substitution before my final exam which has double and triple integrals. YES I know I am screwed, wish me luck
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Why is it that when you plug in the lower limit for the integral with respect to dx (that being 0) it becomes the lower limit with respect to du, instead of it being the upper limit with respect to du (since 16 is greater then 0) - question to do with the worked example @3.37
Antasar Suleman when you swap limits in substitution, you just plug in the values and replace limits. Here it is from 0 to 4 so when x = 0 , u=16 and when x= 4, u= 0 ( from u = 16-x^2) and hence the integral which was from 0 to 4 in terms of x is now from 16 to 0 in terms of u . If you want it to he from 0 to 16 just put a negative sign outside and you can swap the limits
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Do you have a video of U-Substition with Indefinite Integrals?
Yep: ruclips.net/video/sdYdnpYn-1o/видео.html
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Thanks man I forgot I need to change limit too
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Well explained .
Also this video does not have any audio FYI. Still more informative than the prof I'm paying 😂😂
at the first problem, why didn't you substituted u again by the parts of the integrand ? instead you substituted the value of u by the upper and lower limit
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things make so much sense now
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i deadass thought the uu att the beginning was a cause I was watching the vid with no sound until I watched it again for the second time and heard him say u
兄弟，讲得太好了。
The only thing I don't get is what if it can't be simplified?
thats the answer then
Excellent 👍
Hey, thanks for uploading this video! I have a qn. At 1:51 , how come do we not substitute the du? Help me see it, please! Thanks!
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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?
exactly, that’s what i thought!
I love you thanks for the clarification
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
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thanks for making this video
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Thank you
What is the difference between integration by parts with this U- Substitution Rule
this video saved my life
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
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