AC6.4 - 6.4 CONCEPT QUESTIONS, page 437 1. See the...

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6 Integration 542 6.4 CONCEPT QUESTIONS, page 437 1. See the Fundamental of Calculus Theorem on page 429 in the text. 2. See page 433 in the text. a. It measures the total income generated over the ( b a ) days. b. () b a Rtd t EXERCISES 6.4, page 437 1. 4 4 1 1 222 ( 4 1 ) 6 , Ad x x == = = or 6 square units. The region is a rectangle whose area is 3 2, or 6, square units. 2. x x = = z 44 8 4 1 2 2 1 2 -1 , or 12 sq units. The region is a rectangle whose area is 4[2 ( 1)] = 12 sq units. 3. Ax d x x = = z 29 1 8 1 3 2 1 3 , or 8 sq units. The region is a parallelogram of area (1/2)(3 1)(2 + 6) = 8 sq units.
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6 Integration 543 4. Ax d x x x =−+ = + z 1 4 1 8 1 2 1 4 1 4 di or 9/8 sq units. The region is a triangle whose area is (1/2)(3)(3/4) = 9/8 sq units. 5. d x x x =+ = + = + = z () ( ) ( ) 23 3 4 61 3 1 2 1 2 2 1 2 , or 12 sq units. 6. d x x x =− = = = z ( 8 ) 41 2 3 2 4 22 2 2 4 2 2 4 , or 22 sq units. 7. d x x x + = + = + F H G I K J −− F H G I K J = z 2 1 2 3 1 2 4 1 3 4 8 3 8 1 3 4 9 , or 9 sq units. 8. x d x x x =−= −= = z 42 1 3 32 64 3 32 3 3 0 4 0 4 , or 32 3 sq units. 9. A x dx x == = = z 1 212 1 2 1 2 ln ln ln ln , or ln 2 sq units. 10. A x dx x dx x = = + = z z 11 1 4 1 2 1 4 2 2 4 2 2 4 2 4 , or 1 4 sq units. 11. d x x = = z 1 9 32 1 9 2 3 2 3 27 1 52 3 / ( ) , or 17 1 3 sq units. 12. d xx = = z 34 1 3 1 3 1 4 1 4 12 0 (81 ) sq units. 13. d x x x = = = z ( ) ( ) // 8 1 2 1 8 13 3 4 43 8 1 8 1 3 4 1 4 , or 18 1 4 sq units. 14. d x x = = z 1 9 1 9 3 1 4 , or 4 sq units. 15. Ae d x e e = z 0 2 0 2 2 1 , or approximately 6.39 sq units. 16. x d x e xe e e e = = z ( ) ( ) 1 2 2 1 2 2 1 2 2 3 2 1 2 2 or approximately =−+ −− + = , 24 1 1 8 9 8
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6 Integration 544 3.17 sq units. 17. 333 4 2 6 2 4 2 4 dx x z == = () . 18. −= = = z 22 4 2 6 1 2 1 2 dx x .
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This note was uploaded on 03/26/2011 for the course ACCOUNTING 102 taught by Professor Albert during the Spring '11 term at Karachi Institute of Economics & Technology.

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AC6.4 - 6.4 CONCEPT QUESTIONS, page 437 1. See the...

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