The area of the region bounded by the curves
\[
y=2^x,\qquad y^2=4x
\]
and the lines
\[
x=\frac12,\qquad x=1
\]
is
Show Hint
When finding the area between two curves,
\[
\boxed{
\text{Area}
=
\int_a^b
(\text{Upper curve}-\text{Lower curve})\,dx.
}
\]
Always determine which curve lies above the other before integrating.