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TI-Nspire™ CAS

3.6

# Calculus: The Second Fundamental Theorem of Calculus

by Texas Instruments

#### Objectives

Identify the graphical connections between a function and its accumulation function

• For a given function, recognize the accumulation function as an antiderivative of the original function
• Apply and explain the second Fundamental Theorem of Calculus

#### 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. As a result, students will:

• Use the accumulation function with a fixed starting point to find definite integrals of a function over different intervals.
• Observe that the accumulation function is an antiderivative of the original function.
• Apply the antiderivative property of the accumulation function in combination with their use of the accumulation function to determine a definite integral.
• Conclude with stating and applying an informal statement of the second Fundamental Theorem of Calculus.