### Home > APCALC > Chapter 3 > Lesson 3.3.4 > Problem3-136

3-136.

Write a Riemann sum to estimate the area under the cuve for $2\le x\le3$ using $20$ left endpoint rectangles given $f(x)=9x−2$. Then compute the actual area geometrically and calculate the percent error. Homework Help ✎

APPROXIMATE AREA:

Left-endpoint Riemann sum:

$\displaystyle \sum_{i=0}^{n-1}\Delta xf(a+\Delta xi)$

Notice that there will be $20$ rectangles squeezed into a $1$ unit interval. This will be a very small $\Delta x$, and a very good approximation of the area under the curve.

ACTUAL AREA: If you cannot visualize the familiar geometric shape that is formed when you graph $f(x) = 9x − 2$ on $2\le x\le3$, then sketch a graph.

$\text{percent error }=\frac{\text{actual value - approximate value}}{\text{actual value}}$