# How do you estimate the area under the graph of f(x) = 10sqrt(x) from x = 0 to x = 4 using four approximating rectangles and right endpoints?

Feb 25, 2015

Using equal width rectangles, the 5 sides (remember you need 5 sides for 4 touching rectangles) will occur at
$x = 0$, $x = 1$, $x = 2$, $x = 4$, and $x = 4$

The right endpoints of the rectangles will have heights"
$f \left(1\right) = 10$,
$f \left(2\right) = 10 \sqrt{2} = 14.14$ (approx.),
$f \left(3\right) = 10 \sqrt{3} = 17.32$ (approx.), and
$f \left(4\right) = 20$

Since each area has a width of $1$ the total area of the $4$ approximating rectangles is
$10 + 14.14 + 17.32 + 20$
$= 61.46$