Consider the area between the graphs x$+2$y$=1$

and x$+7=$y$^2$

$.$ This area can be computed in two different ways using integrals.

First of all it can be computed as a sum of two integrals

where

$,$

$,$

and

Alternatively this area can be computed as a single integral

where

$,$

and

Either way we find that the area is

$.$