January 22nd, 2014, 02:28 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Finding area by integration
How to find the area of the shaded region? I can't find the answer.

January 22nd, 2014, 04:19 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Finding area by integration
What "region" do you mean? Your graph doesn't appear to make a lot of sense. What is that left boundary? You have the place where the line y= 8 2x crosses it labeled "4". Is that the y value? 8 2x= 4 when 2x= 4 or x= 2. Is the left boundary x= 2? And what is the bottom boundary? I see a "2". Is y= 2 the lower boundary? If all of that is true, rotate it 90 degrees and integrate with respect to y rather than x. From y= 2 to y= 2, the left boundary is x= 2 and the right boundary is the parabola, or . From y= 2 to y= 4, the left boundary is x= 2 and the right boundary is y= 8x 4 or . So the area is given by 

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area, finding, integration 
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