Riemann sum | MIT 18.01SC Single Variable Calculus, Fall 2010

Riemann sum
Instructor: Christine Breiner
View the complete course: ocw.mit.edu/18-01SCF10
License: Creative Commons BY-NC-SA
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[@jsurinderveygal561]

Thank You, it helped a great deal

[@georgesadler7830]

This video is very helpful. The Riemann sum is very helpful in finding areas in Calculus.

[@MultiManux]

You basically want to start @ the original, but then it depends on the
End points which is Left Endpoint and Right Endpoints, usually
Ln starts at 0 and Rn starts with 1, but then again it all depends on the n, lets say if n starts at 5 then you might starts at 5 for the Ln. That's how I understand it...hope someone explains it more clearly :)

[@KgasS]

the objective is summing up the area under curve. If the value is negative we need to take its absolute value. correct if wrong?

[@imperatoreTomas]

i wonder if people from MIT even watch this

[@mittmasai1678]

Am in luv

[@AnthonyPickett]

a square is always a rectangle, but a rectangle is not always a square.

[@1lindy11]

This doesn't seem to me to be a very good approximation unless I am missing something.If you take the integral of X cubed you get one quarter times x to the 4th. then when you plug your limits of integration into that integral you get 84/4 minus 1/4 equals 83/4 which is a long way from 8. Or what did I do wrong?

[@embedded_]

It's a bad approximation ,but if you put 3 in x^4/4 you will get 81/4 ,not 84/4 . Anyway the real area is 20. This is big difference between 20 and 8. Error of approximation is much more than the answer

[@embedded_]

You want to ask- why approximation of area is so bad? So, the answer is simple: x^3 is fast growing function and that the teacher take left end point. As if we didn't take point 3 in the sum, we didn't add 27 to the answer. But in this case we would get 36 instead of 8 - weird result. But this is because we take fast growing function and big Delta x. You can take Delta x for example 0.1 and you will get better result.

[@101sarahh]

When you are putting it into the Riemann Sum notation, why does i=0? Why doesn't it start at -1?
Thanks!

[@rajinfootonchuriquen]

9 years later but sumatory is not define with index of negative value. The sum from this case should be from 0 to 3 + from 0 to 1 and for the last part, you use your index - 1, so when i=0, you get in the function -1

[@TheBritleb]

i love you

[@rdorsey]

I thought I was the only one who felt that way about her.