U-Substitution Example 8 (KristaKingMath)

How to use u-substitution to evaluate a definite integral.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[kristakingmath]

There are two methods of doing these problems. You can either leave the limits of integration alone, and then back-substitute before you evaluate, like I did, or you can change the limits of integration and then evaluate the definite integral with the new limits, without having to back-substitute, which is what you're talking about. Both methods will get you the same answer every time, so do whichever one makes more sense to you! :)

[kristakingmath]

You can if you want to, but you don't have to. If you change the bounds, then you can plug those new bounds in directly after you've done the integration. If you don't change the bounds, then you just have to integrate, then change the equation back to something in terms of x, from something in terms of u. Whichever way is easier for you is the way you should do it! :)

[kristakingmath]

@docdub23 haha...I love you 4. No but seriously, I'm glad you like the videos. :) Without them though, I'm sure you would still do great with Khan.

[kristakingmath]

ln and e cancel with each other, so (ln e)^2 is just 1^2, which is 1. I hope you do great on your test!! :D

[kristakingmath]

I'm sure you did great! And at least it's done with now. :)

[kristakingmath]

@lolkiwi That's awesome! GOOD LUCK with your exam!! :D

[kristakingmath]

awesome!! i'm so glad it helped!! :D

[ReoklessTortuga]

Don't you need to change the bounds of integration when substituting?

[mpaphidzilesotho]

thank you so much. i used to memorize how my lecture did this kind of questions which led to a lot of mistakes during test but now you have simplified everything for me. no nid to memorize solving steps. :)

[jasondelacruz]

(ln e)^2 = 1?y is that try it in my scientific calculator but always error...but in (ln 1) result is as ur thnk i will get the highest score in calculus tom. whahahaha...

[seshen]

I just went through all your U-substitution examples and I can now do any U-substitution they throw at me with confidence :D. Thank you so much for saving my butt!

[sonuuk]

thank you so much for all your videos on integration. they really helped me a lot in my calc exam. God Bless you!

[azeeez]

Thanks for this example, this was in my previous midterm. now i understood it not just memorize it :))

[pspabiel]

thanks for clearing it up for me..the method you did is new to me and kind of easier..thanks again!

[enioni]

you are a good at should consider taking up a job in professional teaching. :-)

[jasondelacruz]

i dnt know if i perfect my exam...but i know i get high grade..THNKYOU alot!

[pspabiel]

dont you change your limits of integration since its a definite integral?

[MrFrankthetank]

I feel great about U-substitution. Can u please do a trig example when you get a chance?

[billwindsor]

Hi Krista, awesome job on all your Calculus videos!! Here, I think when you transition to the u-substitution, I think we need to change the definite integral bounds to the u variable, according to: u = ln x. So the new u-substitution definite integral will have bounds from 0 to 1. But then you transitioned back to x when you actually solved the definite integral (using the original definite integral bounds for x), so your final answer is correct -- so all good on the final answer. (Please feel free to check me on this.) All the best, Bill

[johnfinch]

what happens if the x's don't cancel when you substitute du