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AC6.3 - 6.3 CONCEPT QUESTIONS page 427 1 See text page 424...

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6 Integration 537 6.3 CONCEPT QUESTIONS, page 427 1. See text page 424. 2. See text page 426. EXERCISES 6.3, page 427 1. 1 3 (1.9 + 1.5 + 1.8 + 2.4 + 2.7 + 2.5) = 12.8 3 4.27. 2. 1 4 (4.5 + 8.0 + 8.5 + 6.0 + 4.0 + 3.0 + 2.5 + 2.0) = 38 5 4 . = 9.625. 3. a. A = 1 2 (2)(6) = 6 sq units. b. Δ x = 2 4 1 2 1 2 1 2 3 4 3 2 0 1 = = = = = ; , , , . x x x x A 1 2 [3(0) + 3( 1 2 ) + 3(1) + 3( 3 2 )] = 9 2 = 4.5 sq units. c. Δ x = 2 8 = 1 4 . x x 1 8 0 7 4 = = ,..., . A + + + + + + + 1 4 1 4 1 2 3 4 5 4 3 2 7 4 3 0 3 3 3 3 1 3 3 3 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = 21 4 = 5.25 sq units. d. Yes. 4. a. A = 6 b. x 1 = 1 2 , x 2 = 1, x 3 = 3 2 , x 4 = 2 A = 1 2 1 2 3 2 3 3 1 3 3 2 7 5 ( ) ( ) ( ) ( ) . . + + + = c. x 1 = 1 4 , x 2 = 1 2 , x 3 = 3 4 , ..., x 8 = 2. A 1 4 1 4 1 2 3 4 7 4 3 3 3 3 3 2 6 75 ( ) ( ) ( ) ( ) ( ) . . + + + + + = " d. Yes.
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