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## Class 12 math (India)

### Course: Class 12 math (India)>Unit 10

Lesson 11: Riemann sums

# Comparing areas of Riemann sums worksheet

Practice ordering the areas of a left, midpoint, and right Riemann sum from smallest to largest.

## Problem 1

Let A denote the area of the shaded region shown below.
We can approximate the exact area A using the following Riemann sums. L, left parenthesis, 6, right parenthesis is the left-hand rule with 6 equal subdivisions. M, left parenthesis, 6, right parenthesis is the midpoint rule with 6 equal subdivisions. R, left parenthesis, 6, right parenthesis is the right-hand rule with 6 equal subdivisions.
Put these three approximations in order from smallest to largest.

## Problem 2

Let A denote the area of the shaded region shown below.
We can approximate the exact area A using the following Riemann sums. L, left parenthesis, 6, right parenthesis is the left-hand rule with 6 equal subdivisions. M, left parenthesis, 6, right parenthesis is the midpoint rule with 6 equal subdivisions. R, left parenthesis, 6, right parenthesis is the right-hand rule with 6 equal subdivisions.
Put these three approximations in order from smallest to largest.

## Problem 3

Let A denote the area of the shaded region shown below.
We can approximate the exact area A using the following Riemann sums. L, left parenthesis, 6, right parenthesis is the left-hand rule with 6 equal subdivisions. M, left parenthesis, 6, right parenthesis is the midpoint rule with 6 equal subdivisions. R, left parenthesis, 6, right parenthesis is the right-hand rule with 6 equal subdivisions.
Put these three approximations in order from smallest to largest.

## Want to join the conversation?

• So, it depends on whether the function is increasing or decreasing?