Learning Outcomes
 Use the Fundamental Theorem of Calculus, Part 1, to evaluate derivatives of integrals.
 Use the Fundamental Theorem of Calculus, Part 2, to evaluate definite integrals.
 Explain the relationship between differentiation and integration.
Textbook
 Chapter 5.3 The Fundamental Theorem of Calculus
Textbook Assignment
 p. 562: 170, 171, 177, 182, 183
WeBWork Assignment
 IntegrationFundamental Theorem
Exit problems of the session

Find the derivative using the Fundamental Theorem of Calculus:
(a). (b).  Evaluate following definite integrals.
(a). (b). (c).
Key Concepts
 Fundamental Theorem of Calculus, Part 1:
If is a continuous function over an interval , and the function is defined by
, then .
 Fundamental Theorem of Calculus, Part 2:
If is a continuous function over an interval , and is any antiderivative of , then
.
Videos and Practice Problems of Selected Topics
 The Fundamental Theorem of Calculus (8:02) Connecting differentiation and integration.
 Finding the derivative using the Fundamental Theorem of Calculus (3:23) Find .
 * Practice: Finding the derivative using the Fundamental Theorem of Calculus. (4 problems)
 Definite integrals: reverse power rule (4:13) Find and .
 * Practice: Definite integrals: reverse power rule. (4 problems)
 Definite integrals: rational functions (5:04) Find .
 Definite integrals: radical functions (3:50) Find .
 Definite integrals: trigonometric functions (4:59) Find .
 Definite integrals: logarithmic functions (7:26) Find .
 *Practice: Definite integrals. (4 problems)