Simpson's Approximation (KristaKingMath)

[@aaronseidel1158]

I am a double major in environmental geology and applied mathematics. I work very hard to do well in math, and rely heavily on these online videos. Mostly Khan Academy and Patrick JMT. I came across your videos while i was working on understanding the process of partial fraction decomposition and I was very impressed with you ability to teach the concept. I have subscribed to you and thank you for being a resource for me to learn outside of the classroom. I get A's because people like you who have an exceptional ability to teach are willing to take the time to provide these videos. Thanks!

[@kristakingmath]

+Aaron David You're very welcome, Aaron, and I'm really glad you enjoyed the partial fractions videos. I'm honored to be able to help, thank you so much for subscribing!!

[@kristakingmath]

I'm glad it helps! I hope you can get in, get out, and get on with your english and history! :)

[@VictoriaMcIntyre1]

Thank you for putting this up. Calculus is really tough for me, and I've been struggling to grasp the concepts (I'm more into english and history, so math isn't "my thing"). This is so helpful :)

[@RicardoBiloti]

The approximation provided by Simpson's rule in the this particular example is exact, indeed. It would produce the exact solution even with n=2. Due to the way Simpson's rule is derived, it is exact for every polynomial of degree three or less. So it is not a surprise that the "approximation" yielded in fact the true solution in this case. Of course, as an example of the "mechanics" of the method, it is ok.

[@kristakingmath]

@XxAngelShinn You're welcome! :)

[@bobbydreamsforu]

Hii..You are our divinely gift for integral calculus. So nice to see your videos. Take care.. Satish..

[@radt3989]

So what would you do if the question asks you to do Simpson’s rule but the value of n=9 (or any other odd value)? What would I do?

[@kristakingmath]

Thank you so much! :D

[@southnail]

This is the way advanced-math should be taught, not tedious, intimidating academic method.

[@cameo64]

Since n = infinity is not even, what number is large enough to approximate infinity in a Simpson's approximation? 10^20 ?

[@PramodKumar-cf3tr]

Do you have videos on Ito calculus? if not are you planning to do one.

[@kristakingmath]

I don't have videos yet on Ito calculus, and I likely won't be making them any time soon. Sorry about that!

[@c24c24c24]

can you do a video on calculating the error bound?

[@kristakingmath]

does this help? Taylor's inequality :)

[@PreciousNectar]

Thank you!

[@chancewilson]

If you are doing the integral of x^2 from a to b, why aren't you doing 2x+C from a to b? Or is that only the fundamental theorem of calculus?

[@kristakingmath]

that's only if you're using the fundamental theorem and/or taking the definite integral to find exact area under the curve. in this example, we're using simpson's rule to approximate area, which is a different method.

[@chancewilson]

Thank you

[@plusfort7645]

just a question if we apply simpson 's rule and trapezoidal rule for the same integral and the same n .should we arrive to the same result exactly ??

[@kristakingmath]

+Plus Fort No, you will almost certainly arrive at different results. Trapezoidal rule, Simpson's rule, and Left, Right, and Midpoint rules all work a little differently, and will give you different approximations of the area. One rule is not always the most accurate. The rule that's most accurate depends on the shape of the curve. And the only truly accurate way to find area is to use the integral.

[@plusfort7645]

+CalculusExpert.com thank you so much that's amazing and i wish if there are teachers like you in algeria cause you are make the study more intresting

[@kristakingmath]

you're welcome! :)

[@plusfort7645]

i'am from algeria and i like so much your videos i have seen your methods i'am student of math i like your way of teaching i advanced all my frinds to watch you and i ask you just to put a video about least squares Approximation please i need it and thank you previously

[@kristakingmath]

+Plus Fort I'm glad you like the videos! I do have a video already for least squares approximation, which you can find here: youtube . com / watch?v=1pawL_5QYxE

[@dwightd3659]

I still don't understand why would you multiply with 4,3

[@iduncare99]

thanks u soo much!!

[@mahmoudabdeljawad347]

thanks alot it's really so helpful :D

[@kristakingmath]

i'm so glad it helped!

[@RStheCE]

I preferred the one where we could see you explain it to us :(