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Course: Calculus, all content (2017 edition)>Unit 4

Lesson 8: 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. $L\left(6\right)$ is the left-hand rule with $6$ equal subdivisions. $M\left(6\right)$ is the midpoint rule with $6$ equal subdivisions. $R\left(6\right)$ 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. $L\left(6\right)$ is the left-hand rule with $6$ equal subdivisions. $M\left(6\right)$ is the midpoint rule with $6$ equal subdivisions. $R\left(6\right)$ 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. $L\left(6\right)$ is the left-hand rule with $6$ equal subdivisions. $M\left(6\right)$ is the midpoint rule with $6$ equal subdivisions. $R\left(6\right)$ is the right-hand rule with $6$ equal subdivisions.
Put these three approximations in order from smallest to largest.

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