# Math Help - Finding area between two graphs

1. ## Finding area between two graphs

Consider the area between the graphs and

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 ,

How do I go about doing this? Thanks

2. ## Re: Finding area between two graphs

plot x&#43;9&#61;y&#94;2 and y&#61;11-x - Wolfram|Alpha

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

3. ## Re: Finding area between two graphs

$x = 11 - y$

$x = y^2 - 9$

determine intersection values ...

$y^2 - 9 = 11 - y$

$y^2 + y - 20 = 0$

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

$y = -5$ , $y = 4$

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

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

finish it.