Calc II: What is the I'th Subinterval?

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In summary, the conversation discusses the concept of the ith subinterval in relation to the Riemann integral. It is a way to divide an interval into n subintervals and label them from left to right. The "ith subinterval" refers to the subinterval numbered "i".
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bmed90
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Hello, I've been in calc II for awhile and for some reason I cannot grasp the concept of what is ment by the ith subinterval. I know it has to do with summing up n number of slices. Can anyone please elaborate? Maybe have a simple explanation for what the ith subinterval is ? Thanks
 
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I suspect you are talking about the Riemann integral. To define the integral on some interval [a, b], you divide it into n "subintervals". If you then number them 1, 2, 3, ..., from, say, left to right, you have the "first subinterval", the "second subinterval", etc. The "ith subinterval" is just the subinterval that is numbered "i".
 

1. What is a subinterval in Calc II?

A subinterval in Calc II is a smaller interval within a larger interval. It is used to break down a larger interval into smaller parts for more precise calculations and analysis.

2. How is the I'th subinterval determined?

The I'th subinterval is determined by dividing the larger interval into I equal parts. This can be done by taking the difference between the upper and lower bounds of the interval and dividing it by I.

3. Why is the I'th subinterval important in Calc II?

The I'th subinterval is important in Calc II because it allows for more accurate calculations and analysis. By breaking down a larger interval into smaller parts, we can better understand the behavior and properties of functions within that interval.

4. How is the I'th subinterval used in Riemann sums?

In Riemann sums, the I'th subinterval is used to determine the width of each rectangle used to approximate the area under a curve. The width is equal to the length of the I'th subinterval, and the height is determined by the function at a specific point within that subinterval.

5. Can the I'th subinterval be adjusted in Calc II?

Yes, the I'th subinterval can be adjusted in Calc II. It is a variable that can be changed to increase or decrease the number of subintervals within a larger interval. Generally, the more subintervals used, the more accurate the calculations will be.

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