July 6th, 2017, 10:36 AM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Find the definite integral
Find the definite integral $$\int_{0}^{20}X[X+.5]\,dx,$$ (where X is the greatest integer for [X+.5]) Attempt: I found out that if X> or = to X+.5, then we would have X[X+.5] as our function. And if X<X+.5, then our function would be (X[X+.5]), then I thought about adding up two integrals $$\int_{0}^{X+.5}(X[X+.5]),dx,$$+$$\int_{X+.5}^{20}(X[X+.5])\,dx,$$ but was unable to work through this integral. Last edited by skipjack; July 7th, 2017 at 02:44 AM. 
July 6th, 2017, 11:48 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,763 Thanks: 905  
July 6th, 2017, 11:55 AM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 1,763 Thanks: 905  Quote:
you'll see it's 20 isosceles triangles each $0.5$ tall, and $1$ wide The area of each triangle is just $\dfrac 1 2 (1)(0.5) = \dfrac 1 4$ So 20 of these sum to an area of $5$  
July 6th, 2017, 03:34 PM  #4 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0 
Yes, you wrote it correctly.
Last edited by skipjack; July 7th, 2017 at 02:43 AM. 
July 7th, 2017, 03:12 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,594 Thanks: 1492 
Your attempt (if X $\small\geqslant$ X + .5, etc.) was obviously incorrect.


Tags 
definite, find, integral 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Find the integral  definite  sachinrajsharma  Calculus  1  June 18th, 2013 11:38 PM 
definite integral  panky  Calculus  3  October 26th, 2012 09:23 AM 
Definite integral  BinaryReader  Calculus  3  March 27th, 2012 10:49 PM 
definite integral  stuart clark  Calculus  4  March 17th, 2011 09:01 AM 
Using the definite integral to find motion  funsize999  Calculus  3  June 1st, 2009 02:36 PM 