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**Unformatted text preview: **Lecture Section Objectives Assignment 29 5.4 Area and the Fundamental Theorem of Calculus 5.4: 1-45 eoo, 53, 57, 61-73 odd, 75, 81, 91 Understanding Goals: 1. Understand the definition of definite integral and the difference between indefinite integral and definite integral. 2. Understand how to use the Fundamental Theorem of Calculus to evaluate definite integrals. 3. Understand how to find the average values of functions over closed intervals. 4. Understand how to use properties of even and odd functions to help evaluate definite integrals. 5. Understand how to use definite integrals to solve marginal analysis and annuities problems. We know how to use geometric formulas to find area of simple regions such as rectangles, triangles and circles. How can we find the area of nonstandard regions such as the region R shown in the Figure shown below? 1 Example 1 : Evaluate 3 4 x dx x . \ Proof of the Fundamental Theorem of Calculus Let be a partition of [a, b] with a = x...

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