Introduction to Calculus 2: Area Estimation

Name: Introduction to Calculus 2: Area Estimation
Rating: 4.9 (24 reviews)

Learn the basic method of area estimation: Riemann Sum

Created byGina Chou

Last updated 1/2025

English

What you'll learn

To estimate area under a function and the x-axis
To study the sigma notation and summation rules and formulas
To calculate the signed area

Course content

3 sections • 17 lectures • 1h 27m total length

Overview1:52
Welcome and How It Works0:48
Explore the course structure of this free introductory calculus two module on area estimation, and access valuable lecture notes, upcoming sections, and practical assignments for practicing calculus two.
Tips to Maximize Your Learning0:27

Downloadable Notes0:03
Area Estimation11:25
Explore area estimation under a curve by splitting the interval into subintervals. Use right-endpoint and midpoint rectangles, and sum delta x times height to approximate the area.
Example 2: Area Estimation of Sin Function6:43
Estimate the area under sin(pi x) on [0, 2] using a six-rectangle left-endpoint Riemann sum, revealing a zero signed area as positive and negative parts cancel.
Example 3: Area Estimation Physical Context6:12
Estimate displacement as the area under the velocity curve using right-endpoint rectangles. For v(t)=4−t^2 on [0,3], six subintervals of 0.5 give displacement about 0.625 meters.
Sigma Notation5:47
Learn sigma notation as a language for summing terms, with an index k from start to end, and translate expanded sums into sigma form while spotting patterns.
Summation Rules and Formulas5:03
Examples: Evaluate Summation9:54
Explore how to evaluate summations using standard formulas, expand terms, and apply sum rules across multiple examples from 1 to n, including k squared and product terms.
Limit of a Riemann Sum5:21
Compute the exact area under a continuous function by partitioning [a, b], using right endpoints, summing f(x_k) Δx, and taking the limit as n approaches infinity.
Example 1: Evaluate Signed Area7:24
Compute the signed area under f(x) = x - x^2 on [0, 3] using a Riemann-sum approach. Take the limit as n grows to get the exact value 9.
Example 2: Evaluate Signed Area5:38
Example 3: Evaluate Signed Area12:28
Compute the signed area from 0 to 2 using delta x and base times height sums, derive a general area from 0 to r, and verify with 0 to 2.
Example 4: Evaluate Signed Area7:08
Assignment 1: Riemann Sum

Requirements

Precalculus (algebra, trigonometry, and functions)
Calculus 1 (limits, continuity, derivatives, and their applications)

Description

HOW THIS COURSE WORK:

This course, Introduction to Calculus 2: Area Estimation, includes the first section you will learn in Calculus 2, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and theorems. The course is organized into the following topics:

Area Estimation (Riemann Sum)
Sigma Notation
Summation Rules
Summation Formulas
Evaluating Summation
Limit of a Riemann Sum (Signed Area)

CONTENT YOU WILL GET INSIDE EACH SECTION:

Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.

Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).

Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.

HIGHLIGHTS:

#1: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.

#2: One problem set at the end of the course (with solutions!) for you to do more practice.

#3: Step-by-step guide to help you solve problems.

See you inside the course!

- Gina :)

Who this course is for:

Anyone who has completed calculus 1 (limits and derivatives) and wants to learn some more advanced math
Current calculus 2 students who are looking for extra help outside school
Anyone who is not in science stream but wants to study calculus for fun

Introduction to Calculus 2: Area Estimation

What you'll learn

Explore related topics

Course content

Introduction3 lectures • 3min

Riemann Sums12 lectures • 1hr 23min

Conclusion2 lectures • 1min

Requirements

Description

Who this course is for: