Your first integral is correct.
The second should be .
the instruction says sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. find the area of that region. I'm assuming when it says x=9, area up to x = 9
x=9
points of intersection, x = 0, x =4
y=\sqrt{x} is on top from x = 0 to 4
and on bottom from x = 4 to x = 9
find area using integrals from x = 0 to x = 4 then from x = 4 to x = 9
anti derivative of first integral
antiderivative of 2nd integral
then
area = [F(4)-F(0)]+[F(9)-F(4)]
When I finish all the arithmetic, i get a bunch of square roots... and the answer is 59/12