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Civilization October 30th, 2009 07:57 PM

Area bounded between 2 curves
 
Consider the area bounded between curves y=-2x and y=3-x^{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 - 3-x^2) dx

But then how to proceed?

soroban October 30th, 2009 09:01 PM

Re: Area bounded between 2 curves
 
Hello, Civilization!

Quote:







The graph looks like this:
Code:

                  |
                  *
              *    |    *
          *    *  |    |:::*
  - - * - - - - - * - -|:::|- * - - - -
    *            |  *::::|    *
    *              |      *|    *
                  |          *
  *              |              *
                  |




[color=beige]. . [/color]






But check my work . . . please!


Civilization October 31st, 2009 09:34 AM

Re: Area bounded between 2 curves
 
Whoa, very nice diagram. :D

I actually stopped looking at your post once you typed in (3-x^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. :D After getting the right integrand, integration becomes easier.

Anyway,

A' = 1-2a
2a = 1
a = 1/2

So the lines should be placed at x = 1/2 and x = 3/2, right?


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