The Fundamental Theorem of Calculus

Full solutions (PDFs and videos) are posted on the Friday morning after the assignment is due.

Handouts and Solutions

Video Lessons

Due Week of April 20:
   — Khan Academy Only (no handouts)
Week of April 20
1. Introduction to Antiderivatives
Due Week of April 27:
1. Antiderivative Practice
Week of April 27
2. A Rule for Finding Antiderivatives
3. Riemann Sums Revisited
Due Week of May 4:
2. More Antiderivative Practice
3. Investigating Riemann Sums
Week of May 4
4. Evaluating Definite Integrals with Desmos
5. Properties of Definite Integrals: Combining Regions
Due Week of May 11:
4. Evaluation Practice
5. Combining Regions
Week of May 11
6. More Properties of Definite Integrals
7. Defining Area Functions
Due Week of May 18:
6. More Properties of Definite Integrals
7. Defining Area Functions
Week of May 18
8. Working with Area Functions
9. Definite Integrals with Variable Bounds
Due Week of May 25:
8. Working with Area Functions
9. Definite Integrals with Variable Bounds
Week of May 25
10. Intro to the Fundamental Theorem of Calculus (FTOC)
11. The Fundamental Theorem of Calculus (FTOC): Part 1
12. Definite Integral Practice
Due Week of Jun 1:
10. Intro to the FTOC
11. FTOC: Part 1
12. Definite Integral Practice
Week of Jun 1
13. The Fundamental Theorem of Calculus: Part 2 with Informal Proof
14. The Fundamental Theorem of Calculus: Proof of Part 1
Due Week of Jun 8:

Corrections for Week of Jun 1 + Anything that's late!

Corrections are Due Monday, June 8 before 11:59 PM.
Week of Jun 8

No Formal Lessons! Agenda is TBD (To Be Determined)!

Outline

— We will be introduced to the concept of integrals as the limit of Riemann sums. We will learn to evaluate these limits with Desmos and geometrically (when possible). We will also develop a list of the properties of integrals

— We will use algebra and geometry to discover area functions. We will create area functions to calculate the area under a curve between a fixed number and a variable endpoint. We will recognize the relationship between derivatives and integrals. We will apply the Fundamental Theorem of Calculus.

Goals

• Set up and evaluate integrals to calculate areas.
• Create general area functions.
• Investigate properties of definite integrals.
• Discover and use the Fundamental Theorem of Calculus.
• Calculate area between curves.
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