Calculus: The First Fundamental Theorem of Calculus

Objectives

• Identify the graphical connections between a function and its accumulation function
• Describe the relationship between a function and its accumulation function
• Apply and explain the first Fundamental Theorem of Calculus

Vocabulary

• Signed area
• Accumulation function
• Local maximum
• Local minimum
• Inflection point

About the Lesson

The intent of this lesson is to help students make visual connections between a function and its definite integral. As a result, students will:

• Observe the coincidence of the accumulation function’s extrema with the original function’s zeros, and of the accumulation function’s inflection point with the original function’s extremum.
• Solidify understanding of the relationship between the derivative of the accumulation function and the original function.
• Conclude with explicitly stating the first Fundamental Theorem of Calculus.