Definite Integral (KristaKingMath)

[@b.i.g.j.i.p.s.z.41143]

I am a graduate student at JSU. I am taking Calculus 2 this Summer. This definitely helped alot! Muchas gracias! God bless you for your servitude through your videos to other people!

[@shaktikashyap6]

At 4:56 the way u say "thanks guys" is soo sweet 🤗 and your videos are helpings me a lot for clearing concepts intuitively. Thank you so much🤗.

[@samuelhulin180]

Thank you very much, again. You seem to have a way of explaining things that just makes sense. Whenever my professor confuses the heck out of me, I find your videos and I'm good.

[@kristakingmath]

I'm so glad the videos are helpful!! :D

[@kristakingmath]

@jamin870 Got it! Okay, so you can do one of two things to get rid of it here. If you leave the answer as one fraction, then you'd put (e^2-(1/e^2))/2. OR you can break the final answer into two fractions, in which case, you'd have [(e^2)/2]-[1/(2(e^2))]. Basically, whenever you have something in the numerator with a negative exponent, you just move it to the denominator, and the exponent becomes positive. Really hope that helps, and thanks so much for asking!! :D

[@Sitchy777]

This is the first video ever that has actually helped me with math. Thank you for explaining the steps as you went and not just assuming we knew what was happening.

[@kristakingmath]

+The Saturated Squid You're welcome, I'm so glad it helped!!

[@Sitchy777]

+Krista King | CalculusExpert.com me too xD

[@johncervera2204]

I'm a returning college student and I've been watching your videos for a while now to get through my dynamics course. Honestly I would have not made it this far without your help. Big thanks!!!! Everything has been extremely helpful.

[@kristakingmath]

+Johnny Cervera I'm so glad, and honored to help! Thanks for letting me know, and good luck with the rest of dynamics!

[@kristakingmath]

Ya sorry about that! :/ Some of the earlier videos aren't the best in that regard.

[@almnr81S7]

Integration by substitution. Rule is definite integration of e^x is e^x.

[@lekirie]

Oh my! This is the only video that has the same value of boundaries but with different signs, I've been looking for almost an hour now, thank you so much! I thought I was wrong, phew.

[@kristakingmath]

Sorry about that! I never thought about it, so thanks for pointing it out to me! Glad you like the videos! :D

[@sy4zwanie94]

hi! Im a college student from somewhere in Malaysia and im just watching yr videos just now. My engineering maths assignment is about definite integral and all yr videos abt ths chapter is really2 hv ease my work. Tq pretty math madam ive ever seen! May god bless you 😙😘

[@JacquesMWest]

Thank you very much for your videos. I've watched a couple (basically you're intro to integrals and found them very helpful. Would even say that this matches or exceeds Khan Academy's quality. Thank you very much! Love you lots. :)

[@disneymomz14]

I missed school because I was sick and this is totally helping me understand everything I missed! Thank you!

[@jainagra7515]

how’s life a decade later

[@kristakingmath]

You're welcome! Glad I could help. :)

[@ciitonton6998]

Hi teach ! :) I'm studying Integral Calculus now and a lot of your videos are extremely helping me..Thank you so much and please keep on uploading more videos about Integral Calculus.. thank you :)

[@kristakingmath]

Cii Ton Ton I'm so glad they're helping!

[@ciitonton6998]

integralCALC yeah very helpful..:)

[@ciitonton6998]

integralCALC do you have videos of Indefinite Integrals??or examples about it?

[@kristakingmath]

Cii Ton Ton Here are some simple ones, but I have a lot more! Just search my channel. kzbin.info/www/bejne/o3KsnoGihbieldU kzbin.info/www/bejne/aaivn62vesyFmK8 kzbin.info/www/bejne/nnrEmJx7pb-gmcU kzbin.info/www/bejne/nqDaqZqpfLWnlc0

[@kristakingmath]

@jamin870 What do you mean? What kind of problem are you trying to do? :)

[@bilalahmadbil3999]

thanks dear for giving a brief view of definit integrals i help us much

[@kristakingmath]

+Bilal Ahmad bil You're welcome, I'm glad it helped!

[@kristakingmath]

you're welcome! i'm so glad it's helping! :D

[@claradykstra1114]

Thank you so much for making these videos. You continue to reduce my overall stress levels immensely. Thank you!

[@kristakingmath]

I'm so glad the videos are helping! :D

[@kristakingmath]

Glad I could help! :)

[@kristakingmath]

Awesome! So glad I could help! :)

[@kristakingmath]

Ya, I wish I could go back and change that. :( But at least it's better on the newer videos! :)

[@abrahamthisyear2506]

Thank you for this lesson , it helped understand many things , i'm from Saudi Arabia , I needed some help in Definite integrals and you explained it very well , thanks again . :)

[@kristakingmath]

I'm glad I could help! :)

[@kristakingmath]

Have you checked out the indefinite integral section here? integralcalc (dot) com/indefinite-integrals/

[@kristakingmath]

@cardcollector6794 Wow! Thanks for the kind words :) I'm so happy I'm able to help in some way :)

[@caseyrodriguez5871]

I have my final tomorrow and you have helped me more than all the the videos! Thank you sooo much!!!

[@kristakingmath]

I'm so glad I could help! Good luck on the final!

[@rezaghanbari2479]

You use the word Ummm lot aha! Are you from Texas? Just curious? Thank you it helped me a lot!

[@kristakingmath]

Awesome! Glad you were able to find it. :)

[@kristakingmath]

I wish I could go back and change it! The new videos are better. :)

[@Kalo953]

Simple and clear explanation! Nice video! Could you make one for finding area or volume of trapezoid and some solids with Definite integrals?

[@kristakingmath]

Thanks!

[@Jjacobs1986]

Just started Cal 2. Holy CRAP this is so much more complex than Cal 1's basic limits and derivatives. This video helped a bunch. My college has a 20% first time pass rate for Cal 2. I'm going to LIVE on your channel this semester.

[@kristakingmath]

I hope I can help along the way! Let's make the 20%!! :D

[@caringalkenaldrin1019]

thanks for this..now it is clear and kinda easy to me to handle this definite integral :) thanks to your videos ..i watched it all .thanks again :)

[@adamkite7358]

0:23 I would have preferred the use of 'domain' as opposed to 'range' :)

[@Libbyness]

Thank you for existing

[@katymaclcom9253]

Thank youuu! That is helpful. Am gonna pass my exam after all. Wish my calculus teacher was helpful like u

[@kristakingmath]

you're welcome! good luck on your final!!! :D

[@kristakingmath]

i already have several in addition to this one, but i will add more! :D

[@Postcalculus]

Could you explain the concept of INTEGRATING FACTOR, which is my stumbling block.

[@kristakingmath]

You're welcome! :)

[@hadeerrashad5486]

Excellent explanations!

[@amanmohan635]

Understood thoroughly ! Thanks

[@shaukathuncle3278]

Aman Mohan

[@realtrickybilly]

Thank you. Great video as always.

[@MsReeses97]

thanks for making this video! I was just wondering if you do your videos in order of how it is usually taught or if you created your own order. Thank you so much. Very good video as usual.

[@kristakingmath]

i've done my videos all out of order over the years, but now i've got them in order in my academy. :)

[@kristakingmath]

I like to mix it up. :)

[@muhannadtube]

Please do this : the indefinite itegral of sqrt(1-sqrt(x))/x dx without using partial fractions or by parts techniques.

[@alanmolina4251]

i've just discovered your channel so i havent had an opportunity to look through all your videos, but i have a request that would help address one of the most difficult aspects of calculus: can you make a review video covering the most commonly used algebraic tools in calculus? honestly, that seems to be the most difficult part of calculus and the videos covering calc problems are scarce when it comes to explaining the algebra steps. thank you!

[@kristakingmath]

I will try to make some! Thanks for watching my videos!! :D

[@bl-ands]

Why not simply further by moving the e^-2 from the numerator to the denominator as e^2?

[@saifhasan9451]

i love fact that she is so friendly

[@ds2587]

I wish I found this channel earlier in my semester but better late than never

[@donnamarrylynn5326]

Thank you for sharing Kristaa!! 😝😝 very helpful!

[@kristakingmath]

Aw thanks Donna! Glad it could help. 😊

[@michaelalvarado4046]

thank you very much you are saving my life this semester!

[@kristakingmath]

+Michael Alvarado You're welcome, I'm so glad I'm able to help!

[@baselabbas7949]

Thank you so much , da video is so useful. I can learn more by watching your videos :D

[@kristakingmath]

i'm so glad the videos are helping!

[@unborn29]

Hey,can you plug in that final ans into your calculator & get a constant?

[@super_paperbag]

Can we shift the negative of -e^-2 to the denominator so that we can have the positive power? So the final answer is e^2 / -2e^2?

[@breannaoneal]

Thank you so much! Your video helped a lot and you seem so nice! definitely subscribed (:

[@kristakingmath]

@jamin870 Oh I'm so glad!!! :D Thank you for letting me know, and good luck in your class!! :D

[@kristakingmath]

i won't be able to get to this right away, but you might try plugging it into wolframalpha(dot)com, which will give you the step-by-step solution. hope that helps! :D

[@connorandreatidis7466]

Christian, Harry and I want to say thank you!!!

[@kristakingmath]

thank you so much!! :D

[@sundayquinones6554]

Thank you very much maam, for explaining the complete steps its help me much.

[@kristakingmath]

I'm glad it could help!

[@luisserrano6354]

Oh i understand. This helps a lot! thanks (p.s. We can hear the people trapped in your house. Their screaming is a bit distracting to my learning. 4:49 - 4:52)

[@Gone_AWALL]

This video is great, she just says um a lot!

[@kristakingmath]

Thanks!! :)

[@manasutube1986]

hi thanks can u also help me solving a indefinite integral equation?

[@kristakingmath]

Go and rock the exam! :)

[@kristakingmath]

Love you too! :)

[@syd_jzx100]

You have no idea what that function looks like? It's "e" so of course it's an exponential. And the -2x indicating its flipped and it's a little steeper.

[@Darkine100]

it's been 5 years now I can still remember learning calculus from your videos it was 2012 time flies like anything it's 2016 now and am about to the completion of my btech degree of civil engineering the only reason am at this place it's all becoz of you I still rememberd those days seeking your videos and all I scored 68 out of 100 in the 12 grade mathematics and my parents were very happy with the marks they always asked me about how did you scored so good marks in this mathematics of chse (chse mathematics is regarded as the toughest mathematics in our country it's like like only 30 % students score above 30 mark) I told my parents it was her she taught me mathematics her concept was so freaking clear like only once you have to go through her video and that's it your done calculus is simple as hell man I owe you my life thank you Teacher for everything GOD bless you mam give helping the students you're awesome The only reason why am a civil engineering it's all becoz of you thank you for everything and thank you from my parents too we love you please visit india someday thank you for everything bye

[@kristakingmath]

Wow Darkine, I'm so honored! Really happy to know that I was able to help along the way, and so happy for YOU that you've done so well and are about to complete your civil engineering degree! Congratulations, and good luck in the future, I'm sure you will continue to do amazing things!

[@Darkine100]

+Krista King thank you mam and please keep making videos 😁😁

[@jjjilani9634]

E should not have a negative power. Bring it down to make e^2. -1/2e^2 + e^2/2.

[@1ceQube]

In Example 2 u had zero as ur answer, why dont u have a zero in this solution since u can subtract e^-2 from e^2 ???kind regards Cazzy.

[@MoniMar88]

this helped a lot, thank you!

[@kristakingmath]

+Monica Vargas Yay! Thanks for letting me know!

[@jamelallen5500]

Thanks for making this clear to me :)

[@raulsanchez4716]

Awesome explanation.

[@kristakingmath]

Thank you so much, Sanchez! :)

[@burnage49]

Your videos are very thorough and instructive. You're also so cheerful and gorgeous which makes your videos a pleasant to watch! Also you kind of remind me of Becky from Masterchef US Season 3 :P

[@kristakingmath]

this will tell you a little more about the integrating factor: youtube(dot)com/watch?v=p8yesVjNdzY hope it helps!! :)

[@cesarsuarez2010]

thank you. just the video i was looking for :)

[@CrICSeEe]

why we don't put constant at the end as we do in definite integral.

[@abhimanyuwadhwa6335]

Since we subtract the integral of lower limit from the upper limit, the constant of integration gets cancelled.

[@ChadDrakeTech]

What id there are numbers before the e?

[@noneAsianify]

Krista, but if it's e to the negative 2. Shouldn't the negative 2 go in front?

[@kristakingmath]

the derivative of e^(-2x) is -2e^(-2x). but in this problem, we are taking the integral, which is the opposite of the derivative, which means that we have to divide by the -2 instead of multiply by it, so the result is (-1/2)e^(-2x) instead of -2e^(-2x). :)

[@MegaSumit]

can you tech the maths of cpt (common proficiency test) for ca examination plz ma'am

[@engramjadq]

what a sweet calculus

[@ryandavis7506]

Just started Calc 2 and already forgot how to do this. My book thinks that I have some sort of computer like memory so they leave out the helpful steps. This video literally made my day. One question though; does the Rule 1/k X e^kx only apply to integrals of exponential functions? Seriously I can't remember how to integrate and I just took Calc 1 last semester lol. FML. Thanks in advance for any help :)

[@kristakingmath]

Don't worry Ryan, you can do it! :) That rule applies only to integrating exponential functions. Check out my videos on indefinite integrals, u-substitution, integration by parts, and partial fractions, and that should help jog your memory from Calc 1. Keep your head up, I'm pulling for you! :D

[@utayasurian419]

Thank you for the video which can help me to solve my problems in integral ... :)

[@kristakingmath]

+Utaya Surian You're welcome, I'm so glad it helped!

[@Darkine100]

ur videos are amazing hey I need ur help can u help me with this kinda problems 1. ∫ [x]+x dx 2. ∫ [2x] dx 3. ∫ [xsquare] dx the [] (brackets ) implies they are either +ve or -ve I need ur help before this Friday I have my examination on Saturday i.e on 2 march 2013 pls explain me how I will solve those kinda problems .pls help well I posted this twice cus this is urgent needur help

[@SuperKishlay]

Thank You So much Mam!! This helped me a lot...

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@Darkine100]

pls have a look at this vid and pls explain me how that was formed in both the question mam I need ur help

[@abed031]

i need more lesson from you on definite integral :)

[@SuperMisheru]

But what do you do when you dont know the range? Like if the range went from 0->x?

[@kristakingmath]

You do exactly the same thing! :) You plug in x as the upper limit of integration, and then you subtract whatever you get when you plug in 0, the lower limit of integration. And your final answer will just be in terms of x, instead of being a constant number.

[@SuperMisheru]

Then what if you've got to find the upper limit while knowing the answer? E.g. integrate e^(-3k) = 0,1 when the limits go from 0 to x? I feel like I'm nagging you here, but I just want to be 100% certain that I get it :P

[@kristakingmath]

SuperMisheru It's no problem! But I don't understand the 0,1. What's that supposed to be?

[@SuperMisheru]

integralCALC Here, I'll link to an image of the problem: fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xaf1/v/t1.0-9/10402926_10205204183765365_2134220341788329491_n.jpg?oh=a9f5cbb6f5ffdadc575969e97a355876&oe=54D988AE&__gda__=1427619098_312ab81c285d96380b73839354d12d2d Translated it says: Find the x-value which solves this equation: I solved it, although it took me a million tons of frustration to do so :P

[@kristakingmath]

SuperMisheru Ohhhh... in the US we would write the 0,1 as 0.1. I should have realized that. You would just evaluate the integral and get (-1/3)e^(-3t), and then you would evaluate the result over the interval [0,x] and get (-1/3)e^(-3x) - (-1/3)e^(-3(0)), or (-1/3)e^(-3x) + (1/3)e^0, or (-1/3)e^(-3x) + (1/3)(1), or (-1/3)e^(-3x) + 1/3. Then you'd just solve the equation (-1/3)e^(-3x) + 1/3 = 0.1 for x. So -e^(-3x) + 1 = 0.3, or -e^(-3x) = -0.7, or e^(-3x) = 0.7, or ln[e^(-3x)] = ln(0.7), or -3x = ln(0.7), or x = -[ln(0.7)]/3. In case you didn't already do that, I hope that helps!

[@manasutube1986]

okay i'll try that thanks

[@TrueYears]

my queen

[@kristakingmath]

ha... I don't know about that! But hey.....I'll take the compliment. :)

[@amaansaifi3061]

Great explanation...

[@kristakingmath]

Thank you!

[@manasutube1986]

thanks a lot helped me greatly

[@unicornsum6111]

you're awesome!!thank you

[@kristakingmath]

Aww thanks! :)

[@李康南]

讲得真好❤️

[@aliourangiasr8066]

thank you ,it is a very helpful video.

[@kristakingmath]

Awesome! Glad I could help. :)

[@hyegincho1579]

thank you so much!

[@chedomri6060]

love you!

[@bright7626]

Thank you very much. God bless you.

[@kristakingmath]

+B Whyte Ekans Thank you!