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February 17th, 2013, 09:22 AM  #1 
Member Joined: Aug 2012 Posts: 88 Thanks: 0  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. 
February 17th, 2013, 09:34 AM  #2 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Area bounded by a curve and arbitrary line
First you have to have the following : 
February 17th, 2013, 09:45 AM  #3  
Member Joined: Aug 2012 Posts: 88 Thanks: 0  Re: Area bounded by a curve and arbitrary line Quote:
 
February 17th, 2013, 10:08 AM  #4 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Area bounded by a curve and arbitrary line
Ok , then tell me if you get the final solution right .


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