Difficult# Area Under the Curve

ACTMAT-NXE1OF

The figure below shows the graph of:

$$ f(x) = \sqrt{x}, \ 1 \le x \le 4 $$

The area of the region bounded below by the x-axis, above by $f(x)$, from the left by the line $x = 1$, and from the right by the line $x = 4$ is approximated by trapezoids, as shown below.

What is the approximate area of the region above the x-axis and below $f(x)$ on the interval $ {-1\le x\le 4} $, using the sums of the areas of the trapezoids?