Error Bound Formulas for midpoint and trapezoid rules, sect7.7

[@violabunnie]

I'm taking calc 2 for the second time, and of course, it's online which makes it even harder. My professor barely explains anything (like how to calculate the K value...) You have been an absolute saviour thus far!! I love how you always explain each step and explain very clearly. Thank you so much! I think I can pass the class this time:)

[@blackpenredpen]

Best of luck! You can do it!!

[@malikbodie475]

i know im randomly asking but does someone know of a trick to log back into an instagram account? I was stupid lost the login password. I appreciate any tips you can offer me.

[@ethanwild3301]

@@malikbodie475 they give you log in pins to make it easier

[@Elliot.L87563]

Mine explains everything but very fast, taking it during the summer in high school…..

[@maclancastermusic4757]

God I feel like youre the only calc tutor who explains every single step. I really appreciate you.

[@BITStudioCode]

Bro u r the only tutor that teaches us step by step, my math teacher is like always skipping steps cuz apparently all my other classmates are geniuses and I'm just dumb. Thanks again man!!!

[@markgross928]

I'm taking Calc 2 and am preparing for my second test. Our text (probably the same one you use) has the answers you showed according to the book. I kept coming up with your answer (the more accurate way). I spent 5 hours trying to figure out what I was doing wrong. Then I found your video and now know I had the more correct answer all day! I have watched many of your videos and you do a great job. Thank you for making the videos. The videos have a timeless value. Even 5 years after making this one, it still works for students.

[@blackpenredpen]

Thank you so much Mark! Wishing you the best in your calc class! 😃

[@marygrant5168]

YOU ARE THE ABSOLUTE BEST!!!!!! I got the same answer you got and couldn't for the life of me figure out how the back of the book got their answer. you make this SO clear!!!! thank you so SO SO much!!!!!!!

[@Alex-jf6kl]

You are awesome brother! I read the chapter and I asked my teacher for help but he did a terrible job explaining !! You did it in 7 minutes .. you save me, thank you.

[@reqicide1189]

Thank you, your videos have helped me so much throughout Calc 2. You always have very clear and concise explanations. Wish you were my professor haha

[@worldsavior2543]

Bless your soul, clear and concise.

[@TyronTention]

The book's way almost feels lazy, but the intuition behind it is pretty interesting since you don't have to use a calculator. This video was very helpful.

[@TranquilSeaOfMath]

Very nice. A helpful video. I like that you mention finding the maximal of the second derivative, it is so fast though, it is easy to miss.

[@chovie]

Here I was doing this exact question thinking I was crazy for getting this answer again and again. Thank you for showing both ways to find K! What were they smoking when they wrote this chapter? It's easy to calculate without a graphing calculator, yes, but sooo wrong.

[@robertosaucedo4347]

Thank you!! You are amazing I was doing my homework and keep getting it wrong because I was using the none book way but thanks to you I was able to get my homework done❤

[@sepidehabolfazli7611]

what if we can't use a graphing calculator

[@crowsmathclass]

Check out this video. It works this problem without using a calculator. kzbin.info/www/bejne/hWqToaqBiJeUpas

[@maxpercer7119]

You can use triangle inequality theorem.

[@kennethgee2004]

seems like a recursion issue to me. Went from estimating cos x^2 to estimating some craziness just to get a k value for an estimation. One would need to estimate the maximal again and again, ad infinitum.

[@spik330]

where does the 12n^2 or the 24n^2 come from. My profs notes say that for midpoint on a single interval is (k/4x1-x0))*((x1-x0)/n)^2 and for composite (k/4x1-x0))*((x1-x0)/n)

[@ruizhu5899]

... what should we do to get the max? if we are not allow to use calculator during test and requires to find the K..

[@alvelymondragon33]

i guess just go based off the last bit that he explained 9:43 (how it's solved in the textbook)

[@ruizhu5899]

okok thank you very much@@alvelymondragon33

[@erniez7259]

Is there a way to find k w/o graphing calc.?

[@crowsmathclass]

kzbin.info/www/bejne/hWqToaqBiJeUpas

[@noahcrescini9081]

do you know how come some of the answers online say k=6

[@graoliveira6688]

Excellent explanation, thank you!

[@blackpenredpen]

Happy to help 😃

[@grantnielson9881]

You're the best!

[@hung89341]

What if the question asked to find min number of subintervals of int of (x)dx,x from 1 to 2 for error from true value to be less than 10^-4? Using either Simpson or trapezoid rule.

[@stgr7014]

Hi, Thanks! This was great. What does 'n' represent? Is it number of steps?

[@josephhoneychuck4213]

St Gr n is the number of trapezoidal or rectangles you make when estimating the area under the curve

[@stgr7014]

Thanks!

[@googleuser3323]

Can the error bound be negative? I’m doing some question and it ended up becoming negative... so I’m confused

[@aggffdgubfff]

it can be yes!

[@yandojo]

i love this man

[@bugsbunny278]

What calculator are you using ??!

[@pighast974]

how do you find the bounds when your function's second derivative's max value over the interval is 0?

[@manuelalbertoromero9528]

Yeah, I have that problem as well.

[@DigaDupSuck]

make sure you're taking the absolute value of the second derivative

[@Echoechostar]

what happens if your second derivative is 0? i was given the function 2x-1 and the second derivative = 0, so does that mean K is just 0?

[@theendurance]

yes, it means there is no error bound and the rule will calculate the exact integral

[@Echoechostar]

Mohammad Mahmud wish u replied 4 months ago when I commented this 😂✌🏼😭

[@theendurance]

i just learned that today, had to flex a lil 😂😂😂

[@9MAS91]

Nice job

[@Jadevhn]

Thank you so so much

[@shisirbaral4453]

But why does this formula work at all ?!

[@snowmankiller4222]

much more clear than my porfessor

[@claytonhouser7578]

The calculator way didnt work for me. It just have me some much smaller value

[@DanT-iu6oc]

im starting to love your videos. godDAMN you are GOOD

[@SAYHOP]

Thankyou!!

[@blackpenredpen]

😃

[@Theassociate06]

your calculator is crazy do u charge it 😅

[@andythung]

Book WAY , Sin 1 is not equal to 1, it is 0.01745 ......... k value should be 4 + 2 (0.01745)

[@nikheetisnotcool2951]

He is literally him

[@holyshit922]

uses crt; type TFunc=function(x:real):real; function f(x:real):real; begin f:=cos(sqr(x)); end; function trapezoid(f:TFunc;a,b:real;n:longint):real; var i:longint; h,s:real; begin h:=(b-a)/n; s:=f(a)+f(b); for i:=1 to n-1 do s:=s+2*f(a+i*h); trapezoid:=h*s/2; end; var esc:char; a,b:real; n:longint; begin clrscr; repeat writeln('Podaj przedzial calkowania'); readln(a,b); writeln('Podaj liczbe iteracji'); readln(n); writeln(trapezoid(@f,a,b,n):1:10); (* In some versions of fpc we dont need at operator and function call will look like this writeln(trapezoid(f,a,b,n):1:10); *) writeln; esc:=readkey; until esc=#27; end.

[@cheeng95engineering52]

Mmmmmm... The error bound approach it''s ok ...but a better approach is to use truncation error as shown in this video kzbin.info/www/bejne/moqxXo2Yf9yFoKc ? For me, it makes more sense the use the truncation error in order to estimate the N value for the trapezoidal/Simpsons rules instead of the error bound. Would you agree ? Thanks.

[@CS-bh4ur]

Uhhhh wait a sec English lol jk man but you are talking faster than the speed of sound

[@curtishunt1277]

I love this man