Hello Could you me demostrate some integral inequalities?

[TheDoctor46]

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!

 

[Mute]

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?

 

[TheDoctor46]

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.

 

[HallsofIvy]

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.