U-substitution with integration by parts (KristaKingMath)

[@davewhite5433]

Thanks! You helped me out. And you are the prettiest math teacher ever.

[@rickjames5998]

here voice is so soft. makes math more soothing.

[@bigDeeOT]

Girl you are awesome. My calc book had a problem like this but it never showed how to use the substitution. Now I see why it never showed how to do it, its super easy!

[@Ninjaluke333]

You're great :) I haven't found anyone else on youtube that explains mathematics so effective and simple :D

[@kristakingmath]

Thanks for the kind words :)

[@kristakingmath]

I'm glad I could help! :D

[@kina4288]

Clear as can be. Hallmark of your production.

[@ahmedbilal811]

your videos always help out a lot thanks for all the effort that you put in for us

[@kristakingmath]

You're welcome! I'm so glad I can help. :)

[@HeatherRoseMusician]

Thanks this was very helpful! You have beautiful hand writing!

[@Matt-ye2hg]

For all those who have a test or final tomorrow, Good luck!

[@jordanalcocercorona2342]

Lmaooooo thankssss

[@reenabharath9845]

I am learning now for a test that I have in 20 min

[@crgIN07]

much better than the Stewart text book example

[@briangale404]

Thank you for the video. You made it very easy to follow along.

[@kristakingmath]

Glad you think so! :D

[@Postcalculus]

Although for this problem at wolframalpha, computational time was exceeded, I got the solution to another problem at wolframalpha. Thanks for the link:)

[@javacola25]

why is pi always left alone in final answers? since it has a definite value why can't it be simplified?

[@thomasratliff9278]

Thank you again. This was the perfect pace for me. Not to fast and not to slow. :-)

[@kristakingmath]

You're welcome!!

[@OxLaBelleViexO]

Understand this so much better now. Thank you! Do you have a tutorial video of something like this using substitution with ln or inverse trig functions?

[@kristakingmath]

I'm so glad! :) These might help: U-Substitution Example 8 U-Substitution Example 5 Integrals of Inverse Hyperbolic Functions

[@XPTPCREWX]

Is there a reason why you didn't change the limits of integration during the x substitution process?

[@kristakingmath]

You're right, I should change them to keep them consistent, but most of the time I don't because I'm just going to back-substitute at the end of the problem anyway, and I'll end up changing them right back to what they were originally.

[@XPTPCREWX]

Thanks!

[@rufio171]

integralCALC if you change the limits of integration you don't need to substitute back because you already changed the limits and then you can just plug in for x

[@Grassmpl]

If you don't change the bounds, pls make sure you specify the associated variable. i.e with \theta=.

[@crisatkins8450]

do you have any tutorials on differential equations?? i kinda find it confusing sometimes.. just wondering..thanks:)

[@moodymonstrosity1423]

What??? Aren't cos and thita square a single term??? And thita cube is a orher term so shouldn't we choose between cos thita square and thita cube as to which would be the x substitution?

[@crisatkins8450]

also tutorials related to engineering surveys..please, let me know if you know some links!! thanks,i'd appreciate it!!

[@kevinkoshy246]

This is incredible! THANK YOU SO MUCH!

[@kristakingmath]

You're welcome, I'm so glad you liked it!

[@torqueontwistyroad6275]

I need help...with integral...

[@kristakingmath]

I'm so glad it was helpful! :D

[@kristakingmath]

it's just more accurate to write pi as a representation of it's decimal approximation than it is to round off the decimal value. :)

[@ernestschoenmakers8181]

You made a mistake with the x-substitution concerning the limits cause they should be pi and pi/2..

[@maths656]

incredible. .extraordinary concepts.Thanks for guidance

[@kristakingmath]

You're welcome! I'm glad it could help.

[@curtisreese2958]

Why can't you be my teacher? You're amazing at explaining this stuff. I have followed you since pre-calc and I'm now in calc 2.

[@kristakingmath]

I'm honored! And even though I can't technically be your teacher, I can still be your teacher on KZbin!

[@kevinwang9665]

dont u need to change the boundaries when u do the U-sub?

[@kristakingmath]

You can, but if you end up back-substituting at the end of the problem to put the integral back in terms of the original variable (like I did), then you can leave the bounds the same, instead of changing them and then changing them back. :)

[@m3ma96]

this is very helpful thank you so much

[@melindasingh4628]

This was so helpful! You're amazing!

[@kristakingmath]

+Melinda Singh I'm so glad it helped!!

[@John-yahya]

question : instead of replacing x with theta ^2 , can't we just change the limits of integration into terms of x , and keep the X as it is ? BTW , great explanation ^__^

[@aakash_kul]

Yes, you can do that, but remember, it's all about making it easier for yourself. For this specific problem, it's much easier to substitute x back in instead of solving for the bounds in terms of theta.

[@tingmike3564]

It would be slightly faster to just change the limits of integration. You wouldn't have to rewrite the equation in terms of x. Also, changing the limits of integration is not difficult; plugging in to x= Theta^2 is pretty much what she does at 7:16

[@sweetattack9508]

OMG!!! this helps so much!!!! thank you

[@MrBlash93]

Thank you so much. I really appreciate your help. Extremely helpfull

[@kristakingmath]

You're welcome! :)

[@crisatkins8450]

your tutorials had helped me a lot!!:) just a little volume on the audio would make it nonetheless perfect..thanks anyways!!!

[@randomguy-jp8qj]

I LOVE YOU I FINALLY UNDERSTAND

[@kristakingmath]

:D

[@Aosssamah]

Thanks aloooot ♡,,that was helpful: ) Please can u help me with this Integral of cos(x) x e^x dx

[@Postcalculus]

Hi. Since the computational time was exceeded I solved the problem myself. Here it goes: ∫((x²/(x*sin x + cos x))² dx Let x*sin x + cos x = t => dt = x*cos x. Multiply and divide by cos x and in the numerator take (x²)²= (x³)*x Now rewriting in terms of t and dt: ∫(x³/cos x)*dt/t² Using integration by parts: =(x³/cos x)(-1/t) - (x³/cos x)∫(-1/t) dt =-(x³/cos x)/(x*sin x + cos x) + (x³/cos x)*(ln t) + c Replacing substituents: = (x³/cos x)* ln (x*sin x + cos x) - (x³/cos x)/(x*sin x + cos x) + c

[@vfeeh]

Very helpful, thank you!

[@kristakingmath]

So glad it could help!

[@santhoshkumarp2361]

❤❤❤❤😊😊 Nice one

[@Aosssamah]

I can evaluate it ,,if it was integral of cos(x) e^x dx

[@NBA402]

You could have changed the limits of integration, when you did the x-substitution, to make your life easier, where your integral in terms of x would go from (pi/2) to (pi). Other than that, great.

[@kristakingmath]

Hey! For specific questions like this, try WolframAlpha(dot)com. It will give you step-by-step solutions for this kind of stuff. Hope that helps!! :)

[@kristakingmath]

you should try wolframalpha . com. it should give you the step-by-step solution! :D

[@kristakingmath]

hey! i don't have any videos on engineering surveys, but i have quite a few on differential equations. check out: integralcalc(dot)com/#differential equations. hope that helps! :)

[@frankieh9233]

now i love math hahahah thanks soooooooooooo much !!!!

[@gregoryhoutz7464]

It was incorrect for her to repeatedly write the original integration limits once the substitution of x = theta squared was made. Each step must be mathematically correct. Either drop the limits and work with an indefinite integral or change the limits to [ pi/2 to pi] in the substituted integral. In fact, it would have been better to just change the limits immediately and then evaluate once the IBP was complete. Would have saved steps and writing all those radicals.

[@femzfemz111]

You are so awesome. I got the exact tip i needed. You are so pretty. Pretty and intelligent, that's complete

[@DanielConvalescence]

I thought you had to change the limits since you use u-sub

[@kristakingmath]

You have two options to deal with the limits of integration. You can either change them when you make the substitution, and then you'll be able to evaluate using those limits at the end of the problem (this is the method you're suggesting), or you can leave the limits as they are, back-substitute to get the result back in terms of x, and then use the original limits of integration to evaluate at the end of the problem (this is the method I used). Both methods will get you to the same correct answer. :)

[@kristakingmath]

hahaha you bet!! :)

[@Postcalculus]

Standard computation time exceeded...

[@johnmichaeltwist5086]

Sure. But as soon as you change to "x" the LIMITS OF INTEGRATION must reflect this change as well!!!

[@tc3sean]

+John Michael Twist +calculusexpert.com Yeah, don't we need to change the Limits because we made a substitution? The answer is correct though per stewart solution guide. Oh, because we sub back in our original substitution we don't need to touch our limits!

[@johnmichaeltwist5086]

Sean Ashcraft Got to write things consistently. Change the expression, then limits have to be written changed too. This is mathematics.

[@herbcruz4697]

I agree that she should have changed the limits of integration, in which case, she would have gotten (pi/2) and pi, respectively. However, she did revert back to the original variable, which is another way to do a definite integral by a u-substitution.

[@bigDeeOT]

Because if you simplify it by writing out the answer you won't get the exact answer unless you write it out to a trillion decimal places.

[@Chris-nq3ri]

You are SO cute ma'am for a teacher I am taking Differential Equations Honors at San Jacinto

[@Aosssamah]

Please please help me ♡

[@berkk1993]

your left eye is bigger than the other one