# Calculus Riemann Sums and Sigma Notation with Lesson Video (Unit 6)

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### Description

**Riemann Sums, Sigma Notation and Writing Area as a Limit Lesson:**

Your AP Calculus students express the limit of a Riemann sum in integral notation and write integral notation as a limit of a Riemann sum.

**What is included in this resource?**

⭐ Guided Student Notes

⭐ *Fully-editable* SMART Board® Slides

⭐ Google Slides®

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Video Lesson Link for Distance Learning - Flipped Classroom models

⭐ Full solution set

**Lesson Objective:**

★ Express the limit of a Riemann sum in integral notation

★ Write integral notation as a limit of a Riemann sum

**College Board® Topics:**

Topic 6.3: Riemann Sums, Summation Notation, and Definite Integral Notation

**College Board® Learning Objectives:**

**LIM-5:** Definite integrals can be approximated using geometric and numerical methods.

**LIM-5.B:** Interpret the limiting case of the Riemann sum as a definite integral.

**LIM-5.C:** Represent the limiting case of the Riemann sum as a definite integral.

**LIM-5.B.1:** The limit of an approximating Riemann sum can be interpreted as a definite integral.

**LIM-5.B.2:** A Riemann sum, which requires a partition of an interval *I*, is the sum of products, each of which is the value of the function at a point in a subinterval multiplied by the length of that subinterval of the partition.

**LIM-5.C.1:** The definite integral of a continuous function *f* over the interval [*a, b*], is the limit of Riemann sums as the widths of the subintervals approach 0.

**FUN-5.C.2:** A definite integral can be translated into the limit of a related Riemann sum, and the limit of a Riemann sum can be written as a definite integral.

**The unit includes:**

1) Approximating Area With Riemann Sums

2) Sigma Notation and Riemann Sums

4) Properties of Definite Integrals

5) Antiderivatives & Indefinite Integration

6) The Fundamental Theorem of Calculus

7) Integration By Substitution

8) Integration of Transcendental Functions

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**AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.**

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