If you have a table that includes f(x) values, like f(x_0), f(x_1), f(x_2), etc., then you can just plug those into the trapezoidal rule formula. Instead of having to plug the x values into a function to find the f(x) values, and then plug those into the formula, the f(x) values have already been found for you, so you can just go straight to plugging those into the formula. :)
I never got to thank you for saving me in Calc 1, so thank you so much!! Now I am in Calc 2 and I only go to class for attendance. I read the book and watch your videos when I need help... because this is the only way I actually understand things to do homework and pass exams. Thank you so much for being passionate about what you do and teaching so many students :)
@ChannelLAMCO You'll see this formula written different ways, and each way is probably acceptable. You could take away the 2s, and the 1/2 on the outside, and just multiply 1/2 by the first and last term inside the brackets, and that would be a mathematically equivalent formula to the one I wrote here. You just need to pick one, and stick with it. Hope that helps! :)
You deserve a trophy or a statue or something ridiculous in your honor for the work you do here. Your explanation of Taylor polynomials, in particular, rocked my world... Thank you so much for taking the time.
I just researched how to do the trapezoidal rule and coincidentally the text I used had a similiar problem except my n=5. Your method is an interesting variation on what I learned. I like that since I can compare results which helps me catch my own errors. If two correct methods that yield a true answer are used, then I have a warning to rework my problem and therefore minimize errors on my part. This is practical for real world problems. Thanks for your usual fine lesson. Take care.
Hi! So, I am a 4th-year geophysics undergrad at Baylor Univ., and I just want to say that this video (and multiple others) have really helped over the years. Whether that's review or learning something altogether new, this channel has truly helped. Doesn't matter how old you are or where you're learning, stuff like this helps. Thanks:)
I think that you are a good lecturer. You can explain a boring maths in easy way. It's look so interesting. I hope you still doing this things to students around the world who can access youtube. Thank you very much.
Good video, step-by-step solutions are always great help, and i'm sure everyone would agree :) Also, the reason why the terms after and before the last terms are multiplied by 2, is because they are used twice. given an simple example from the interval 1 to 5, with n =4, the trapezoids are the following: [1,*2*] , [*2*,*3*] , [*3*,*4*] , [*4*,5] notice the first and last, aka 1 and 5, are only used once, while the others are used twice.
Sammy Morini just for my knowledge i wanted to ask if u could tell me that, is this formula independent of the number of segment the trapezoid is being divided in?
Wow, you made this so much easier to understand. Thank you for taking the time to do these videos, I have actually used several of your videos to better understand Calculus concepts, so a huge thank you for what you do!
I am VERY thankful she does these videos. I am just VERY annoyed that she is constantly taking up room where she should be doing math and sometimes I can't even see the board
Thanks Krista: you help me a lot .have been looking for how to solve trapezoidal questions until I found this video. You explained it in details that make it simple for me to solve any questions from trapezoidal. THANKS ONCE AGAIN
you are right. it looks terrifying in the textbooks. Thanks for this wonderful lecture, but you should have included the error estimates of the trapezoidal rule. sorry if my English is poor :)
where did you get the number 2 from? I can't figure out why some people use 2 while others use (1/2)... is there something that determines what to multiply the middle intervals by?
What if there is no function to plug the number into like your doing at around 7:02? Our teacher gave us a table with x from 0 to 10 (& the f(x) from 0 to 10 ), and then told us to find the trapezoidal rule approximation for it using 10 subintervals? Idk what to do? Can anyone help? Please and thank you.
Best explanation of the trapezoidal rule on youtube !! Thanks 4 posting this ^_^ Btw did anyone ever tell you that you look like Anna Kendrick because u look soooo much like her ! :O
+Jeffrey Cheng x_0 just represents "the first x value" where you're going to evaluate. So it could change depending on which rule you're using. For example, if you used Riemann sums with left endpoints, then x_0 would be the left edge of the interval, but if you used Riemann sums with right endpoints, then x_0 would be the right edge of the left-most rectangle.
@TheTalkeetna1 I'd be happy to do everything I can to help you with DiffEQ. Check out my DiffEQ videos on RUclips to get started, or you can see everything I've done so far, arranged by topic, on my website: integralcalc(dot)com. :)
As usual I tried to read about this in the Calc book, and as usual I gave up and came here. Now I get it! What I do not get is the three thumbs down ratings. If you don't like looking/need to look at mathematical videos, then don't look at them. I wouldn't go somewhere, order liver and onions and then give the food a thumbs down because I hate liver. I plan on using this as a valuable (yet free!) learning tool through Calc3.
As you can see in the videos to the right there are plenty of math videos with males that are in the video. You should be thankful that she is even doing this for free for you and also that she responded to you so kindly. >:l
Why do none of these videos show how to do it as a summation? I need to be able to do it as a summation for my calc 2 class and I keep seeming to get it wrong. For a small n (
+BWO Josh You'll probably need to write out the first few terms of your series, and then generate your own sum, kind of like I do in this video where I talk about how to "collapse" the series into a sum: ruclips.net/video/r7c44AmdlEY/видео.html
because that's the trapezoidal rule formula. since you're dividing the area into trapezoids, adjoining trapezoids share a side, and so you multiply by 2 to account for that side twice. :)
Krista King In practice, you take half of the first and last terms, leave the middle terms alone, sum the set, and multiply the result by ∆x. It's less complicated, reduces operations, and reduces the error term when dealing with large datasets.
If you have a table that includes f(x) values, like f(x_0), f(x_1), f(x_2), etc., then you can just plug those into the trapezoidal rule formula. Instead of having to plug the x values into a function to find the f(x) values, and then plug those into the formula, the f(x) values have already been found for you, so you can just go straight to plugging those into the formula. :)
I never got to thank you for saving me in Calc 1, so thank you so much!! Now I am in Calc 2 and I only go to class for attendance. I read the book and watch your videos when I need help... because this is the only way I actually understand things to do homework and pass exams. Thank you so much for being passionate about what you do and teaching so many students :)
You're so sweet, I'm honored! Good luck with the rest of calc 2, I know you'll do great!!
Absolutely. You can use Simpson's or Trapezoidal, even Riemann sums, to find the area under the curve. :)
@ChannelLAMCO You'll see this formula written different ways, and each way is probably acceptable. You could take away the 2s, and the 1/2 on the outside, and just multiply 1/2 by the first and last term inside the brackets, and that would be a mathematically equivalent formula to the one I wrote here. You just need to pick one, and stick with it. Hope that helps! :)
You deserve a trophy or a statue or something ridiculous in your honor for the work you do here. Your explanation of Taylor polynomials, in particular, rocked my world... Thank you so much for taking the time.
not yet, but i think there are some others on youtube. and i'm working on adding one soon! :)
YOU'RE WELCOME! :) It makes me so happy knowing the videos are helping.
You just taught me what my teacher didn't teach me and because of that you got one more subscriber.
Thank you so much for the comment! :D
is there a video to find error bounds?
I'm so glad I was able to help! :)
I just researched how to do the trapezoidal rule and coincidentally the text I used had a similiar problem except my n=5. Your method is an interesting variation on what I learned. I like that since I can compare results which helps me catch my own errors. If two correct methods that yield a true answer are used, then I have a warning to rework my problem and therefore minimize errors on my part. This is practical for real world problems. Thanks for your usual fine lesson. Take care.
Exciting! I'll keep my fingers crossed for you! Let me know how you do... :)
@Angelakake You're very welcome! :)
That's so awesome! Thanks for following up and letting me know! :D
So glad I could help! :)
Hi! So, I am a 4th-year geophysics undergrad at Baylor Univ., and I just want to say that this video (and multiple others) have really helped over the years. Whether that's review or learning something altogether new, this channel has truly helped. Doesn't matter how old you are or where you're learning, stuff like this helps. Thanks:)
+Nathan Benton Aw thanks for the comment, it means a lot! I'm so glad I've been able to help along the way. :)
I hope it went well for you! :D
I think that you are a good lecturer. You can explain a boring maths in easy way. It's look so interesting. I hope you still doing this things to students around the world who can access youtube. Thank you very much.
Sorry about that!! All my new videos are math only, no me. I hope that will be better for you! :D
@RayPatron You're welcome!! :D
Good video, step-by-step solutions are always great help, and i'm sure everyone would agree :)
Also, the reason why the terms after and before the last terms are multiplied by 2, is because they are used twice.
given an simple example from the interval 1 to 5, with n =4, the trapezoids are the following:
[1,*2*] , [*2*,*3*] , [*3*,*4*] , [*4*,5]
notice the first and last, aka 1 and 5, are only used once, while the others are used twice.
Sammy Morini just for my knowledge i wanted to ask if u could tell me that, is this formula independent of the number of segment the trapezoid is being divided in?
Wow, you made this so much easier to understand. Thank you for taking the time to do these videos, I have actually used several of your videos to better understand Calculus concepts, so a huge thank you for what you do!
I'm so glad the videos have been helpful! Thank you so much for letting me know. :)
@Pi0666 You're welcome!! :)
I hope so! Let me know when you find out. :)
@idkbcuz You're welcome!! :)
Have you had a chance to see my latest video examples? They just show the screen. :)
You LOVE this formula! Thanks for all the help!
I'm just happy I can help. :)
I am VERY thankful she does these videos. I am just VERY annoyed that she is constantly taking up room where she should be doing math and sometimes I can't even see the board
Thanks Krista: you help me a lot .have been looking for how to solve trapezoidal questions until I found this video. You explained it in details that make it simple for me to solve any questions from trapezoidal.
THANKS ONCE AGAIN
You're welcome, I'm so glad I could help!
You're welcome, I'm so glad it's helpful! :)
You're welcome! Good luck on your finals!! :)
Thanks for letting me know! :)
Thanks!
@jonathankaneking Thank you, and you're welcome!! I hope that exam went/goes really really well!!! :D
you're welcome! GOOD LUCK on your test!! :)
you are right. it looks terrifying in the textbooks. Thanks for this wonderful lecture, but you should have included the error estimates of the trapezoidal rule. sorry if my English is poor :)
Muy bien. Saludos desde Ecuador. You're the best teacher. Great.
where did you get the number 2 from? I can't figure out why some people use 2 while others use (1/2)... is there something that determines what to multiply the middle intervals by?
my book says the formula for the trapezoid rule starts with b-a/2n (instead of just n in the denominator). I trust you, but im confused..?
thank you mam ...ur videos always helped in understanding the matehmatical topics...
:D
oh my god u r the best math teacher in the world....
This is so much better when you have a cutie teaching it instead of a grumpy old man!
What if there is no function to plug the number into like your doing at around 7:02? Our teacher gave us a table with x from 0 to 10 (& the f(x) from 0 to 10 ), and then told us to find the trapezoidal rule approximation for it using 10 subintervals? Idk what to do? Can anyone help? Please and thank you.
You're welcome!
how to find n if it is not given in question ?????????
Thank you so much u really helped me understand the whole topic in depth, great teacher! God Bless :)
Love the way you teach
Best explanation of the trapezoidal rule on youtube !! Thanks 4 posting this ^_^
Btw did anyone ever tell you that you look like Anna Kendrick because u look soooo much like her ! :O
thanks!! i'm so glad it helped!! :)
Out of curiosity, since n is even, is it also possible to do Simpson's Rule?
do you have any vids on the error bound for the trap rule ?
thanks to your video, i finally get this part. I'm preparing for my final Cal1 test tomorrow,so thank you
you're welcome! good luck on your final, i hope you do great!
how to find n if it is not given in the question?
Awesome!! I'm so glad it helped!! :D
@TheIntegralCALC oh I see. Thank you so much for your help!
Will do! :)
You've saved my butt many times in Calculus! God bless you and your Fighting Irish :)
:D
thanks for your help
you're welcome!
@dang822 I'm so glad! And thank you so much! You are so sweet!! :)
I wonder how accurate this approximation is?
love it! ur my fave tutor!
Thank you for helping us
+maher fz You're welcome!
What if your N doesn't end up with the upper value b?
Oh awesome!! I'm so glad!! :D
@G0OS3 Glad I could help! :)
I was wondering if Simpsons and Midpoint Rule have the same X bar values? is x sub 0 in Trapazoidal rule the same in the other rules?
+Jeffrey Cheng x_0 just represents "the first x value" where you're going to evaluate. So it could change depending on which rule you're using. For example, if you used Riemann sums with left endpoints, then x_0 would be the left edge of the interval, but if you used Riemann sums with right endpoints, then x_0 would be the right edge of the left-most rectangle.
May you please show how to do this on a calculator?
Thank you so much!!
Hey, thank you very much. This is a good review for my finals :D
thank also.. really help me to understand in simple way.. keep up the good work.. :)
Awww! Thank you!! :)
Awww, thanks!
Thanks! Good luck with you're final year. :)
Thanks a lot superb explanation
You're welcome, and thank you!
@TheTalkeetna1 I'd be happy to do everything I can to help you with DiffEQ. Check out my DiffEQ videos on RUclips to get started, or you can see everything I've done so far, arranged by topic, on my website: integralcalc(dot)com. :)
love this video and the rest that you have on her about cal 2
As usual I tried to read about this in the Calc book, and as usual I gave up and came here. Now I get it! What I do not get is the three thumbs down ratings. If you don't like looking/need to look at mathematical videos, then don't look at them. I wouldn't go somewhere, order liver and onions and then give the food a thumbs down because I hate liver. I plan on using this as a valuable (yet free!) learning tool through Calc3.
They probably didn't like the way she explained it.
@eLiAsSoCcEr I can be your teacher! Well....sort of, just on here I guess. :) Glad I was able to help.
As you can see in the videos to the right there are plenty of math videos with males that are in the video. You should be thankful that she is even doing this for free for you and also that she responded to you so kindly. >:l
This video is great! It helped alot.
I have one qus in trapezoidal rule .i have no n value how i find pls tell tomorrow exam😢
Thank you
Great video. Thanks for the help with my exam :-)
thanks your work is amazing!
you're welcome!! :)
Why do none of these videos show how to do it as a summation? I need to be able to do it as a summation for my calc 2 class and I keep seeming to get it wrong. For a small n (
+BWO Josh You'll probably need to write out the first few terms of your series, and then generate your own sum, kind of like I do in this video where I talk about how to "collapse" the series into a sum: ruclips.net/video/r7c44AmdlEY/видео.html
why are you multiplying the terms in the middle by 2?
because that's the trapezoidal rule formula. since you're dividing the area into trapezoids, adjoining trapezoids share a side, and so you multiply by 2 to account for that side twice. :)
Krista King In practice, you take half of the first and last terms, leave the middle terms alone, sum the set, and multiply the result by ∆x. It's less complicated, reduces operations, and reduces the error term when dealing with large datasets.
Thats a cool way to hold the pen :D thanks for the videos youve me helped a lot ma'am
I wish you had found it earlier too! But better late than never. :)
Thank u so much u helped me ... plz keep doing this ...
because delta x is b-a/n already that's why she divide the delta x with 2 to make it b-a/2n :)
thanks dear for helping
+sohaib sattar You're very welcome!
@ennraii Thank you so much!! :)
The more trapezoids you use, the more accurate it becomes! :)
Hey..could u plzz tell me..is this taught in high schl or clge in USA??
Wish my professor make it this easy to understand. =]]
Thank you so much! The amount of times you've saved me is ridiculous!!! :D :D :D
:D
Awww THANKS! :D
Awwww thanks! :)