Make visual connections between a function and its definite integral.

• Students will be able to identify the graphical connections between a function and its accumulation function.
• Students will be able to describe the relationship between a function and its accumulation function.
• Students will be able to apply and explain the first Fundamental Theorem of Calculus.
• Use appropriate tools strategically. (CCSS Mathematical Practice)
• Look for and express regularity in repeated reasoning. (CCSS Mathematical Practice)

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

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.