CPM Homework Help : CALC Problem 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.

Hint 1:

APPROXIMATE AREA:
Left-endpoint Riemann sum:

Hint 2:

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.

Hint 3:

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.