How to Find a Definite Integral using Riemann Sums and the Limit Definition: Quadratic Example

  Рет қаралды 100,617

The Math Sorcerer

The Math Sorcerer

2 жыл бұрын

In this video we go through all the steps of evaluating a definite integral using the limit process. The example chosen for this video is a quadratic with three terms. We look at the definite integral of x^2 + 2x - 5 from 1 to 4. This is not the hardest example but it's also not the easiest. I hope this is helpful.
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Пікірлер: 89
@kimjay9064
@kimjay9064 Жыл бұрын
I really love how you provide formulas unlike other teacher who just simply teach teach directly
@TheMathSorcerer
@TheMathSorcerer Жыл бұрын
Yeah you definitely need the formulas for problems like this. It's a super good idea to write down the formula always before doing the problem. Good luck:)
@water9713
@water9713 5 ай бұрын
No teacher does that. They have to go over formulas before solving 😂😂😂
@mattarcarese6136
@mattarcarese6136 2 жыл бұрын
Absolute alpha chad when it comes to math and calculus. Great job, man.
@naimas9161
@naimas9161 2 ай бұрын
I love this style of teaching! Providing baby steps (basic math) and explaining how you simplified things in detail makes a big difference for me.
@Vauxiinyourbag84
@Vauxiinyourbag84 2 ай бұрын
I know right, people need to do more of this shit. I actually understand it a bit more now!
@smashingstuff2454
@smashingstuff2454 Ай бұрын
I agree because I taught myself alot of calculus for my fall semester coming up for 2024 of calculus to prepare. Calculus is alot but I noticed talking baby step and baby the problem especially limits it makes it alot easier to solve.
@tonyayad5629
@tonyayad5629 2 ай бұрын
I know this video is two years old and there are a ton of comments but the way you worked this out was amazing. I have hated this Riemann guy for the past 3 months but you made it too easy. Thank You The Math Sorcerer!!!
@jaydee4541
@jaydee4541 2 жыл бұрын
Your work is clear, concise, and very helpful. I like the fact that you don't skip steps and your presentation speed is easy to follow. I've gained a lot through watching your video. Thanks so much!
@memt8147
@memt8147 5 ай бұрын
it is so over
@sufma6505
@sufma6505 26 күн бұрын
same my finals tmr im cooked
@CarlosRegular
@CarlosRegular 25 күн бұрын
Inshallah my brother 🫡🙏🏻
@justsumm8156
@justsumm8156 12 күн бұрын
I'm cooked bro
@Austin-bk4ul
@Austin-bk4ul 6 ай бұрын
I reckon I speak for a lot of university students when I say that I wish for you nothing but the best life has to offer. You have no idea how much your explanation saved my life and helped me unstress about upcoming tests. You truly deserve success in life
@LucasDimoveo
@LucasDimoveo 2 жыл бұрын
Perfect timing. I'm officially learning integrals now!
@TheMathSorcerer
@TheMathSorcerer 2 жыл бұрын
Perfect!
@ahmedfarah4094
@ahmedfarah4094 Ай бұрын
How did it go
@betsualuna3364
@betsualuna3364 Жыл бұрын
Omggggg this video was super helpful, I was stuck on a problem for over an hour and thanks to you I finally got it !
@vladus8014
@vladus8014 4 ай бұрын
The funniest calc video I've seen in a while, thx man
@akosk385
@akosk385 2 ай бұрын
All I can say is thank you and mail you a vial of my tears - bless you!
@stevebob240
@stevebob240 2 ай бұрын
Thanks for walking through this. I totally relate to messing up the basic addition at the end too.
@tmann986
@tmann986 Жыл бұрын
Just felt like reviewing Riemann sums 😊 I don’t want that skill to go away!
@DXTR_likesrap
@DXTR_likesrap Жыл бұрын
Dudes having a blast
@douglasstrother6584
@douglasstrother6584 2 ай бұрын
Some Old School Math Sorcerer!
@danielshin4515
@danielshin4515 10 ай бұрын
The trick of dividing 27/n^3 * n(n+1)(2n+1) towards the end has been the answer I was looking for, Thank you
@rinuya
@rinuya 8 ай бұрын
This video is also perfectly applicable for any function of higher degree x, given that you are provided the formula for the sum of i^x. Amazinigly explained, thank you!
@david.hilbert1234
@david.hilbert1234 Жыл бұрын
Perfect time. I'm learning Riemann Integral with a perfect man of Mathematics !
@hakimi3380
@hakimi3380 Жыл бұрын
u helped me understand riemann sum, thank you so much!!
@NamaleBarbra
@NamaleBarbra 2 ай бұрын
U r beyond the best... thanks so so much 😊
@Monica-in6mk
@Monica-in6mk 2 жыл бұрын
thank you this video saved me to understand this topic!
@thejuicedorange9317
@thejuicedorange9317 Ай бұрын
BRO NOT A SINGLE VIDEO HELPED UNTILL THIS ONE WHAT A UNIT
@pauloeliasdiaz
@pauloeliasdiaz 7 ай бұрын
This video is pure gold, thanks
@SnoreBaby
@SnoreBaby Жыл бұрын
thank you so much for making it simple!
@dingfro7612
@dingfro7612 2 жыл бұрын
I've got an exam in an hour and this video felt like it helped a lot, lets hope it goes well
@erdenkalilayev3877
@erdenkalilayev3877 Жыл бұрын
did it bro? 😂
@sardarbekomurbekov1030
@sardarbekomurbekov1030 2 жыл бұрын
Awesome. It helped me refresh Reiman integration.
@albamichelle9100
@albamichelle9100 Ай бұрын
You are the reason I am passing my calc test, thank u!
@katebobrusev9037
@katebobrusev9037 10 ай бұрын
Thank you! Very helpful!
@fatmabegumdurmaz5657
@fatmabegumdurmaz5657 5 ай бұрын
Thank you so much! Before watching that video I was hopelessly staring at my textbook now I totally understand the point! Thank you sir, you are amazing 🤩
@user-uy1sl8rz8h
@user-uy1sl8rz8h 7 ай бұрын
Awesome explanation sir ❤
@lawliet2263
@lawliet2263 2 жыл бұрын
Hey math sorcerer, can you recommend some good books on infinite series? Particularly which includes alternating harmonic series
@pabloa2228
@pabloa2228 Жыл бұрын
Is it me or is it just beautiful how it works….
@muhammadbinuzair2101
@muhammadbinuzair2101 2 ай бұрын
Thank you so much❤
@IG_Nice
@IG_Nice Жыл бұрын
Thank you so much🙏🏻🙏🏻🙏🏻🥰
@daniella9498
@daniella9498 2 ай бұрын
amazing video!!!
@user-sm4ol1sl6s
@user-sm4ol1sl6s 5 ай бұрын
THANK YOU SOOOO MUCHHH
@mackaybrendle4665
@mackaybrendle4665 8 ай бұрын
the only example I can actually understand
@kaylalow7080
@kaylalow7080 Жыл бұрын
My last 4 brain cells left after calculus 2 short-circuited the rest of them greatly thank you kind sir
@therenaissanceman8392
@therenaissanceman8392 Жыл бұрын
THANK YOU!
@lusianelundu2702
@lusianelundu2702 9 ай бұрын
Bro keeps laughing 😂 Thank youuu sir❤❤
@joryferrell7244
@joryferrell7244 7 ай бұрын
Can anyone explain why we only need to multiply by the leading coefficient? I get that the cubed n's cancel out...but why do we not need to multiply by the 1's and add them?
@jsbsbsj715
@jsbsbsj715 5 күн бұрын
Thanks
@nickpirkle5370
@nickpirkle5370 2 жыл бұрын
just saved me so much time by seeing this video. Only thing for me is you didn't add the limit notation until the end, but other than that this clarified a ton of stuff for me. Thanks so much.
@TheMathSorcerer
@TheMathSorcerer 2 жыл бұрын
happy that this video helped someone!
@thomasblackwell9507
@thomasblackwell9507 Жыл бұрын
MAJOR LEAGUE FLASHBACK! HAPPINESS!!!!
@kazuakihatano2238
@kazuakihatano2238 7 ай бұрын
I was just curious but is this affected if the partitions weren't spread out evenly at all?
@violethill4454
@violethill4454 5 ай бұрын
sir what if the "n" subintervals are given, what would be the solution process?
@walter-st3fb
@walter-st3fb Ай бұрын
helpful!
@walter-st3fb
@walter-st3fb Ай бұрын
is this a possible ap calc question
@lawliet2263
@lawliet2263 2 жыл бұрын
Good stuff
@user-wv6bb4ps7j
@user-wv6bb4ps7j 4 ай бұрын
Why are we allowed to multiply 3/n into the rest of the Riemann Sum at 7:35?
@ashlees3718
@ashlees3718 Жыл бұрын
thank you :)
@lionheart1330
@lionheart1330 Жыл бұрын
Using a 1000 rectangles it sums to 21.0285045, 24.966942 and 29.2837545 left, mid and center respectively.
@peasant8246
@peasant8246 5 ай бұрын
The function you are integrating goes from negative to positive inside the interval of integration. Shouldn't you have split it in two parts around the zero point?
@TG-to5nf
@TG-to5nf Жыл бұрын
How did you evaluate those summations to get [n(n+1)(2n+2)]/6 etc.
@photonaut_8875
@photonaut_8875 Жыл бұрын
They are mostly formulas you have to memorize , for me anyways. Numberphile did a good video that helped me understand called 1- 1 million.
@ugwunnadiobioma123
@ugwunnadiobioma123 5 ай бұрын
How did this formula come about and who discovered it ?
@bmdiscover7827
@bmdiscover7827 Жыл бұрын
For this; You are the bridge between Georg Friedrich Bernhard Riemann and us.
@Ka_TAB
@Ka_TAB 5 ай бұрын
I owe him my life 🤧
@darcash1738
@darcash1738 7 ай бұрын
To make sure you didn't make any mistakes with formulas, you can generalize the last part before taking the limit like this: Term with i squared: Resulting coefficient over 3. Term with i, first power: Resulting coefficient divided by 2 Term with no i: Same as the resulting coefficient from multiplying by ∆x So, you can think of it as dividing by 3, 2, and 1(or doing nothing) respectively! (But then of course you might have wanted to just integrate like normal to begin with then i suppose)
@justas6494
@justas6494 2 жыл бұрын
crazy stuff
@noonespecial3536
@noonespecial3536 3 ай бұрын
But what happens when n approaches infinity? That part makes no sense. You just do some stuff and end with whole numbers. HOW??
@Pittbull13
@Pittbull13 10 ай бұрын
I am 59( 30 years ago) and I still have nightmares about calculus. I made a C and I never worked so hard to get a C. I wish I had a professor like you. I will have to say that as a corporate credit manager I have never used calculus(not even once) ha
@michelle50915
@michelle50915 Ай бұрын
Can I ask how would you apply this if you were doing the left or right endpoints?
@tear728
@tear728 2 жыл бұрын
I wish my math professor back in the day was more like you, instead of a Chinese man that barely spoke English. He was also a jerk and half the class literally got up and protested half way through class one day lol
@lawliet2263
@lawliet2263 2 жыл бұрын
Man Chinese are best at math in the world, lol they aren't good at learning other languages
@Kurt-kb5oz
@Kurt-kb5oz 25 күн бұрын
This is the n...my friend.
@jessicatidd5491
@jessicatidd5491 Жыл бұрын
i fucking love u bro
@talz8284
@talz8284 Жыл бұрын
Me too! YOU JUST LIKE ME FR
@user-yp1rg2jr5z
@user-yp1rg2jr5z Жыл бұрын
Evaluate {1/(1+x)dx}by this process...I wanted to solve it but I couldn,t...
@lusianelundu2702
@lusianelundu2702 9 ай бұрын
❤❤❤❤❤❤
@Kurt-kb5oz
@Kurt-kb5oz 25 күн бұрын
This is the n....my friend.
@dalitsomvula3474
@dalitsomvula3474 3 күн бұрын
I will make it I have an exam in 1hr 30min
@Vexeis
@Vexeis Жыл бұрын
Baller
@dumbfproductions6105
@dumbfproductions6105 Жыл бұрын
if this comment gets seen by anyone, I would appreciate some insight as to why when I solve this integral using power rule and FTOC I get 51. I plugged this one into two different online math engines and got 21 and 51 respectively. whats going on with that?
@TG-to5nf
@TG-to5nf Жыл бұрын
If you have f(x) ending in -5 you get 21, if you have f(x) ending in +5 you get 51
@munzursu5402
@munzursu5402 16 күн бұрын
I literally have a midterm in 10 minutes
@cathywillies1927
@cathywillies1927 3 ай бұрын
For a moment i thought i*2 is imaginary 😅.
@akaommu
@akaommu 2 жыл бұрын
what was done at @11:48 can you please explain ?! @themathsorcerer
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