May 8th, 2009, 05:39 PM  #1 
Member Joined: May 2009 Posts: 58 Thanks: 0  Definite Integrals, extrema
Find and classify the relative maxima and minima of f(x), if f(x) = integral from 0 to x of {(t^24)dt} /{1+(cost)^2} I got x=2 and x=2 for f'(x)=0, but, I don't know how to calculate the relative maxima and minima. Please help me. Thank you 
May 9th, 2009, 09:07 AM  #2 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: Definite Integrals, extrema
Here, we may use the fact that (As you move to the right, the rate of change of the area under a curve is equal to the height of the function.) Your solutions are correct. To prove that they are relative maxima and minima, we can use the Second Derivative Test: 
May 10th, 2009, 04:53 AM  #3 
Member Joined: May 2009 Posts: 58 Thanks: 0  Re: Definite Integrals, extrema
Thanks for your help. But, how can I calculate f(2)? is x=2 also a solution since the domain of f(x) is x>=0 ?

May 10th, 2009, 05:23 AM  #4 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: Definite Integrals, extrema
If the domain is, as you say, , then is the only local extremum. However, since is squared and added to in the denominator, is defined everywhere. I just put the integral into the Wolfram Online Integrator and it gave an answer that was not expressed in terms of elementary functions. If the problem only asks to classify the extrema, then I don't think you have to worry about the values of the extrema at those points. 

Tags 
definite, extrema, integrals 
Search tags for this page 
definite integral is extremum,indefinite integral finding relative maxima and minima,finding local extrema of integrals,finding the extrema of an integral,integral extrimum,find the extreme of the intergrate,definite calculus(maxima and minima)
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Definite integrals  Agata78  Calculus  6  January 19th, 2013 03:05 PM 
definite integrals  Agata78  Calculus  18  January 18th, 2013 01:39 PM 
Definite integrals  jakeward123  Calculus  10  February 28th, 2011 01:18 PM 
Definite integrals  Aurica  Calculus  2  May 10th, 2009 05:05 PM 
definite integrals  Agata78  Abstract Algebra  0  January 1st, 1970 12:00 AM 