Activities

Objectives

• Students will be able to identify the graphical connections between a function and its accumulation function.
• For a given function, students will recognize the accumulation function as an antiderivative of the original function.
• Students will be able to apply and explain the second Fundamental Theorem of Calculus.
• Construct viable arguments and critique the reasoning of others. (CCSS Mathematical Practice)
• Look for and make use of structure. (CCSS Mathematical Practice)

Vocabulary

• accumulation function
• definite integral
• antiderivative

About the Lesson

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

• Students will use the accumulation function with a fixed starting point to find definite integrals of a function over different intervals.
• Students will observe that the accumulation function is an antiderivative of the original function.
• Students will apply the antiderivative property of the accumulation function in combination with their use of the accumulation function to determine a definite integral.
• The lesson concludes with students stating and applying an informal statement of the second Fundamental Theorem of Calculus.
• This lesson is designed to follow the lesson The First Fundamental Theorem of Calculus.