# Riemann sum

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### Introduction

### Examples

#### Lessons

**Finding the area under the graph of a function using a graphing calculator.**

Consider the function $f\left( x \right) = {x^2}$, $1 \le x \le 3$.

Find the area under the graph of $f$ using a graphing calculator.**Finding the area under the graph of a function using the Riemann Sum.**

Consider the function $f\left( x \right) = {x^2}$, $1 \le x \le 3$.

Estimate the area under the graph of $f$ using four approximating rectangles and taking the sample points to be:**Evaluating integrals with a Riemann Sum**

Consider the function $f\left( x \right) = {x^2} - 5x + 3$, $2 \le x \le 5$.**Evaluating Riemann Sum with trapezoids**

Consider the function $f\left( x \right) = {x^2}$, $1 \le x \le 3$. Estimate the area under the graph of $f$ using four approximating trapezoids.