Consider the area between the graphs $x+2y=19$ and $x+5=y^2.$ This area can be computed in two different ways using integrals.

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

${\displaystyle \underset{a}{\overset{b}{}}}f$

where $a=,$ b $$

and

$f(x)=$

$$

$g(x)=$

$$

Alternatively this area can be computed as a single integral

${\displaystyle \underset{}{\overset{}{}}}h(y)dy$Alternatively this area can be computed as a single integral

${\displaystyle \underset{}{\overset{}{}}}h(y)dy$

where $=,=$ and

$h(y)=$

$$

Either way we find that the area is $$