Hello Could you me demostrate some integral inequalities?

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Homework Help Overview

The discussion revolves around demonstrating certain integral inequalities without calculating the integral itself. The specific inequality in question is between the values 1/3 and 1, concerning the integral of the function (x−3)/(x+5) from 4 to 7.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to prove the inequalities without direct calculation of the integral. The original poster attempts to express the bounds in terms of integrals and considers breaking down the fraction for analysis.

Discussion Status

Some participants have suggested that demonstrating the integrand's behavior within the specified bounds could lead to a resolution. There is an ongoing exploration of potential theorems or methods that could be applicable to the problem.

Contextual Notes

The original poster has not provided a detailed attempt at solving the problem, which is a requirement for further assistance according to forum rules. There is a focus on proving the inequalities rather than calculating the integral directly.

TheDoctor46
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So could you please help me demonstrate some inequalities? Please! They want to prove them without calculating the integral.

1/3<=integral from 4 to 7 (x−3)/(x+5)dx<=1Thanks!
 
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This is a homework-style question, so by the rules of the forum you need to demonstrate some sort of attempt at solving the problem yourself before we can help you.

What have you tried so far? Do you know any theorems which may be useful here?
 


I tried writing 1/3 as the result of an integral from 4 to 7, or 1, but wirh no results. I also tried breaking the fraction, but also, it led nowhere.
 
1/3= (1/9)(7- 4) and 1= (1/3)(7- 4) so if you can show that the integrannd always lies between 1/9 and 1/3, you are done.
 

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