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February 17th, 2013, 09:22 AM   #1
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Area bounded by a curve and arbitrary line

Find the values of m for y = mx that enclose a region with y = x / (x^2 + 1) and find the area of this bounded region.

So I set the two functions equal to each other to solve for x in terms of m:



So when x = 0 and:



Now to solve for m, replace with :



So at y = 1x or y = x, it intersects the graph y = x / (x^2 + 1) exactly. Looking at the graph, if the slope is less steep, it looks like it will create a region. I don't know how to mathematically show this. So I would guess between 0 < m < 1 (not inclusive I guess?) it will create a region. And for the area, the integral I set up is:



Because it's symmetrical I guess. Evaluating:



So the area is:

for 0 < m < 1

Not sure where I went wrong here.
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February 17th, 2013, 09:34 AM   #2
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Re: Area bounded by a curve and arbitrary line

First you have to have the following :


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February 17th, 2013, 09:45 AM   #3
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Re: Area bounded by a curve and arbitrary line

Quote:
Originally Posted by zaidalyafey
First you have to have the following :


Oh, that makes sense. So if I plug it back into the original equation I should get 1 = 1. So then I'm just going in circles and not sure what to do
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February 17th, 2013, 10:08 AM   #4
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Re: Area bounded by a curve and arbitrary line

Ok , then tell me if you get the final solution right .
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