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

3-136.

Write a Riemann sum to estimate $A(f, 2 ≤ x ≤ 3)$ for $f(x) = 9x − 2$ with $20$ left endpoint rectangles. Then compute the actual area geometrically and calculate the percent error.

APPROXIMATE AREA:
Left-endpoint Riemann sum:

Notice that there will be $20$ rectangles squeezed into a $1$ unit interval. This will be a very small $Δx$, 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 $2 ≤ x ≤ 3$, then sketch a graph.