Sketch the region bounded by the curve $f(x) =\sqrt { x }$ and the $x$-axis for $4 ≤ x ≤ 9$.

1. Draw a typical rectangle in the sketch and describe how the height and width are determined.

   Hint (a):

   $Δx$ is the width, and $f(x+Δxi)$ is the height

2. Set up and evaluate an integral to find the area of the region.

   Hint (b):

   as $Δx→0$, $f(a+Δxi)→$__________