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

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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Thank you:)

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I really love how you provide formulas unlike other teacher who just simply teach teach directly

[@TheMathSorcerer]

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:)

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I know right, people need to do more of this shit. I actually understand it a bit more now!

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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]

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!!!

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[@LucasDimoveo]

Perfect timing. I'm officially learning integrals now!

[@TheMathSorcerer]

Perfect!

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How did it go

[@tmann986]

Just felt like reviewing Riemann sums 😊 I don’t want that skill to go away!

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Omggggg this video was super helpful, I was stuck on a problem for over an hour and thanks to you I finally got it !

[@danielshin4515]

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

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[@stevebob240]

Thanks for walking through this. I totally relate to messing up the basic addition at the end too.

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Dudes having a blast

[@rinuya]

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!

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Perfect time. I'm learning Riemann Integral with a perfect man of Mathematics !

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u helped me understand riemann sum, thank you so much!!

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I've got an exam in an hour and this video felt like it helped a lot, lets hope it goes well

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Hey math sorcerer, can you recommend some good books on infinite series? Particularly which includes alternating harmonic series

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[@lawliet2263]

Good stuff

[@mackaybrendle4665]

the only example I can actually understand

[@nickpirkle5370]

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]

happy that this video helped someone!

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helpful!

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Thanks

[@joryferrell7244]

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?

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MAJOR LEAGUE FLASHBACK! HAPPINESS!!!!

[@user-wv6bb4ps7j]

Why are we allowed to multiply 3/n into the rest of the Riemann Sum at 7:35?

[@kazuakihatano2238]

I was just curious but is this affected if the partitions weren't spread out evenly at all?

[@lionheart1330]

Using a 1000 rectangles it sums to 21.0285045, 24.966942 and 29.2837545 left, mid and center respectively.

[@walter-st3fb]

is this a possible ap calc question

[@violethill4454]

sir what if the "n" subintervals are given, what would be the solution process?

[@darcash1738]

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)

[@ugwunnadiobioma123]

How did this formula come about and who discovered it ?

[@peasant8246]

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?

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I owe him my life 🤧

[@bmdiscover7827]

For this; You are the bridge between Georg Friedrich Bernhard Riemann and us.

[@TG-to5nf]

How did you evaluate those summations to get [n(n+1)(2n+2)]/6 etc.

[@photonaut_8875]

They are mostly formulas you have to memorize , for me anyways. Numberphile did a good video that helped me understand called 1- 1 million.

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[@noonespecial3536]

But what happens when n approaches infinity? That part makes no sense. You just do some stuff and end with whole numbers. HOW??

[@user-yp1rg2jr5z]

Evaluate {1/(1+x)dx}by this process...I wanted to solve it but I couldn,t...

[@michelle50915]

Can I ask how would you apply this if you were doing the left or right endpoints?

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This is the n...my friend.

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I will make it I have an exam in 1hr 30min

[@dumbfproductions6105]

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]

If you have f(x) ending in -5 you get 21, if you have f(x) ending in +5 you get 51

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Now also prove the limit just for extra overkill 😅

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I literally have a midterm in 10 minutes

[@cathywillies1927]

For a moment i thought i*2 is imaginary 😅.

[@akaommu]

what was done at @11:48 can you please explain ?! @themathsorcerer