October 30th, 2009, 06:57 PM  #1 
Newbie Joined: Oct 2009 Posts: 4 Thanks: 0  Area bounded between 2 curves
Consider the area bounded between curves y=2x and y=3x^{2}. If 2 vertical lines that are a unit apart intersect this certain bounded area, where should they be placed so that they contain the most amount of the area between them? What's the max. area? I keep getting told that this is the rule I am supposed to use: But I am unsure of how to apply the rule here. Ok so the latex isn't working ... int a  b (2x  3x^2) dx But then how to proceed? 
October 30th, 2009, 08:01 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Area bounded between 2 curves Hello, Civilization! Quote:
The graph looks like this: Code:  * *  * * *  :::*   *      *  ::: *     *  *:::: * *  * *  * *  *  [color=beige]. . [/color] But check my work . . . please!  
October 31st, 2009, 08:34 AM  #3 
Newbie Joined: Oct 2009 Posts: 4 Thanks: 0  Re: Area bounded between 2 curves
Whoa, very nice diagram. I actually stopped looking at your post once you typed in (3x^2 etc.) in the integral from a to a+1. It was easy for me to figure out what the A equals to after having the equation written. Do you have any tips on how to actually start an integration problem like this? Obviously on a test I won't have any help. After getting the right integrand, integration becomes easier. Anyway, A' = 12a 2a = 1 a = 1/2 So the lines should be placed at x = 1/2 and x = 3/2, right? 

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