Area between Curves: Find Area Enclosed by y=x-1 and y^2=2x+6

[samona]

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

 

[Mathoholic!]

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 symmetry 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.

 

[samona]

Thank you!