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## Class 12 math (India)

### Unit 10: Lesson 12

Riemann sums with sigma notation

# Riemann sums in summation notation

AP.CALC: LIM‑5 (EU), LIM‑5.B (LO), LIM‑5.B.2 (EK)
You might need: Calculator

## Problem

The following graph shows a Riemann sum:
Function f of x = x cubed is graphed. The x-axis goes from negative 0.5 to 2. The graph is a curve. The curve starts in quadrant 3, moves upward through (0, 0), continues upward concave up and ends in quadrant 1. The region between the curve and the x-axis, between x = 0 and x = 2, is shaded. The shaded region is divided into 6 rectangles of width 1 third. Each rectangle touches the curve at the top left corner.
Which of the following approximates the area between f, left parenthesis, x, right parenthesis and the x-axis on the interval open bracket, 0, comma, 2, close bracket using a left Riemann sum with 6 equal subdivisions?