Interval of the Riemann integral value

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Discussion Overview

The discussion revolves around finding an interval for the value of a specific Riemann integral involving the function $\tfrac1{\sqrt{4-x^2-x^3}}$. Participants explore methods to estimate the integral's bounds and discuss the behavior of the function over the interval from 0 to 1.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant suggests that the integral might be larger than 0 due to the function being positive on the interval from 0 to 1.
  • Another participant notes that the function $\tfrac1{\sqrt{4-x^2-x^3}}$ increases on the interval $0\leqslant x\leqslant 1$, identifying the minimum and maximum values at the endpoints of the interval.
  • Some participants confirm the approach of using the function's behavior to estimate the integral's bounds, but there is a question about the correctness of this method.

Areas of Agreement / Disagreement

Participants generally agree on the increasing nature of the function within the specified interval and the approach to estimate the integral's bounds, but there is uncertainty regarding the correctness of the proposed solutions.

Contextual Notes

The discussion does not resolve the mathematical steps necessary to definitively establish the bounds of the integral, and assumptions about the function's behavior may depend on further analysis.

goody1
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Hello everyone, I have to find an interval of this Riemann integral. Does anybody know the easiest way how to do it? I think we need to do something with denominator, enlarge it somehow. My another guess is the integral is always larger than 0 (A=0) because the whole function is still larger than 0 on interval from 0 to 1. Thank you in advance.
 

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The function $\tfrac1{\sqrt{4-x^2-x^3}}$ increases on the interval $0\leqslant x\leqslant 1$. The minimum value occurs when $x=0$, and the maximum at $x=1$. You can use that to get estimates for $A$ and $B$.
 
Opalg said:
The function $\tfrac1{\sqrt{4-x^2-x^3}}$ increases on the interval $0\leqslant x\leqslant 1$. The minimum value occurs when $x=0$, and the maximum at $x=1$. You can use that to get estimates for $A$ and $B$.
I tried this. Is that corect solution?
 

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goody said:
I tried this. Is that corect solution?
Yes, that is what I had in mind. :)
 

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