Home > CALC > Chapter 3 > Lesson 3.3.4 > Problem 3-136
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. Homework Help ✎
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.