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Homework Help: Area between curves

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data

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

    3. 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:

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Mar 10, 2012 #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: Mar 10, 2012
  4. Mar 10, 2012 #3
    Thank you!!!!!!!! :smile:
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