Area between curves

  • Thread starter samona
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  • #1
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Homework Statement



Find the area enclosed by the line y = x-1 and the parabola y^2 = 2x+6



The Attempt at a Solution


This is Example 6 in Jame's Stewart Calculus Early Transcentals 6E. I'm trying to figure out why he states that if we were to integrate with respect to x instead of y, then we would have had to split up the region in two pieces.

I'd appreciate it if someone could help clarify that statement.

The link to the example is:

http://books.google.com/books?id=xU...QHNsrzYDw&ved=0CFwQ6AEwCQ#v=onepage&q&f=false

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
You would have to split the region between the graphs in two pieces mainly because the second equation (y2=2x+6), when solved for y, reveals a simmetry along the x axis. You would have to integrate (-(x-1)+(2x+6).5) between a and b (which you calculate) and 2(0-(-(2x+6).5)) between a and c. With c<b.
 
Last edited:
  • #3
19
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Thank you!!!!!!!! :smile:
 

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