Finding area between two graphs

Consider the area between the graphs http://math.webwork.rochester.edu:80...9866f8d281.png and http://math.webwork.rochester.edu:80...7b15d68f41.png

I know how to do this problem by doing it as a sum of two integrals but what I am stuck on putting it together as one function

Alternatively this area can be computed as a single integral

where http://math.webwork.rochester.edu:80...19ca0ec061.png , http://math.webwork.rochester.edu:80...d84f51ed91.png

http://math.webwork.rochester.edu:80...fc8412fef1.png

How do I go about doing this? Thanks

Re: Finding area between two graphs

plot x+9=y^2 and y=11-x - Wolfram|Alpha

As you can see, you need to split it up into two integrals.

Re: Finding area between two graphs

$\displaystyle x = 11 - y$

$\displaystyle x = y^2 - 9$

determine intersection values ...

$\displaystyle y^2 - 9 = 11 - y$

$\displaystyle y^2 + y - 20 = 0$

$\displaystyle (y + 5)(y - 4) = 0$

$\displaystyle y = -5$ , $\displaystyle y = 4$

area = integral of (right curve - left curve) ...

$\displaystyle A = \int_{-5}^4 (11-y)-(y^2-9) \, dy$

finish it.