Proving Bounds for a Riemann Sum: Part II

So you don't need to do anything else.In summary, the conversation is discussing a Riemann sum question involving the function f(x)=x^3/2 and the finite sum Sn. The question asks for suitable upper and lower Riemann sums for the interval [0,100] to prove that S99<J<100. The conversation also mentions finding integer lower and upper bounds for S100, with the use of the integral from 0-100 x^3/2dx.
  • #1
ronho1234
34
0
this is a riemann sum question and i need help with part 2

let Sn denote the finite sum 1+2^ 3/2 +...+n^ 3/2

i) use suitable upper and lower riemann sums for the function f(x)=x^3/2 on the interval [0,100] to prove that S99<J<100

ummm i did this and found 40000<J<41000

II) hence, or otherwise, find integer lower and upper bounds, no more than 1000 units apart, for S100

ummm i don't understand what the question is asking me...
 
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  • #2
Do you mean S99< J< S100 rather than S99< J< 100? And what is 'J'? You don't seem to have defined it anywhere.
 
  • #3
yes i meant S100 and J is from the first part
Calculate J= the integral from 0-100 x^3/2dx which i found to be 40000 i think which leads onto the next two questions
 
  • #4
Well, from your description, it seems you already did #2 , by finding a lower

bound of 40000 and an upper bound of 41000, since their difference satisfies

the condition.
 

FAQ: Proving Bounds for a Riemann Sum: Part II

1. What is a Riemann sum?

A Riemann sum is a method used for approximating the area under a curve on a graph. It involves dividing the area into smaller rectangles and finding the sum of their areas.

2. What is the purpose of proving bounds for a Riemann sum?

The purpose of proving bounds for a Riemann sum is to determine the accuracy of the approximation. By finding upper and lower bounds, we can determine how close the Riemann sum is to the actual area under the curve.

3. How do you prove bounds for a Riemann sum?

To prove bounds for a Riemann sum, you need to use mathematical techniques such as the Mean Value Theorem and the Intermediate Value Theorem. These theorems help in finding upper and lower bounds for the Riemann sum.

4. What is the difference between upper and lower bounds for a Riemann sum?

Upper bounds for a Riemann sum are the maximum possible value that the Riemann sum can take, while lower bounds are the minimum possible value. These bounds help in determining the accuracy of the approximation.

5. Can bounds for a Riemann sum be proven for any type of curve?

Yes, bounds for a Riemann sum can be proven for any continuous curve. However, the techniques used for proving these bounds may vary depending on the shape of the curve.

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