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MS-Sol-EE-C09

# MS-Sol-EE-C09 - CHAPTER 9 DEFINITE INTEGRATION Section 9.1...

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CHAPTER 9 DEFINITE INTEGRATION EXERCISE 9.1 Section 9.1 Definite integrals (page 359) 1. 1 0 1) + (3 dx x = 1 0 2 + 2 3 x x = 3 2 1 2 ( ) + 1 = 5 2 2. 7 4 5 dx = [5 x ] 7 4 = 5(7) – 5(4) = 15 3. - - 3 2 ) 2 (7 dx x = 3 2 2 ] 7 [ - - x x = [7(3) - 3 2 ] - [7( - 2) - ( - 2) 2 ] = 30 4. 20 13 dx = 20 13 1 dx = [ x ] 20 13 = 20 – 13 = 7 5. - - - 1 3 2 5) + 4 3 ( dx x x = 1 3 2 3 ] 5 + 2 [ - - - x x x = [( - 1) 3 - 2( - 1) 2 + 5( - 1)] - [( - 3) 3 - 2( - 3) 2 + 5( - 3)] = 52 6. - - 2 1 3 ) 6 4 ( x x dx = [ x 4 – 3 x 2 ] 2 1 - = [2 4 – 3(2 2 )] – [(–1) 4 – 3(–1) 2 ] = 6 116

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CHAPTER 9 DEFINITE INTEGRATION 7. dx x x ) ( 3 27 8 3 2 - = 27 8 3 4 3 5 4 3 5 3 - x x = - - - ) 8 ( 4 3 ) 8 ( 5 3 ) 27 ( 4 3 ) 27 ( 5 3 3 4 3 5 3 4 3 5 = 77.85 8. - - + 5 1 2 1 ) 8 ( x x dx = [ln x – 8 x –1 ] 5 1 = - 5 8 5 ln – (ln 1 – 8) = 5 32 5 ln + 9. dx x x x - 4 1 4 3 2 2 = - - - 4 1 1 2 ) 2 ( dx x x = 4 1 1 ] ln 2 [ x x - - - = [ - 4 - 1 - 2 ln 4] - [ - 1 - 1 - 2 ln 1] = 3 4 - 2 ln 4 10. + 25 4 1 3 x x dx = - + 25 4 2 1 2 1 ) 3 ( x x dx = 25 4 2 1 2 3 ] 2 2 [ x x + = [2(25 2 3 ) + 2(25 2 1 )] – [2(4 2 3 ) + 2(4 2 1 )] = 240 11. - - 2 2 4) (3 1) + (2 dx x x = - - - 2 2 2 4) 5 6 ( dx x x = 2 2 2 3 4 2 5 2 - - - x x x = - - - - - - - - ) 2 ( 4 ) 2 ( 2 5 ) 2 2( 4(2) ) 2 ( 2 5 ) 2 ( 2 2 3 2 3 = 16 12. 2 1 3 2 1 - - + x x dx = - - + + 1 3 4 2 1 2 x x x dx = 1 3 3 3 3 1 ln 2 3 1 - - - - + x x x = - - - + - - - - - + - - - 3 3 3 3 ) 3 ( 3 1 3 ln 2 ) 3 ( 3 1 ) 1 ( 3 1 1 ln 2 ) 1 ( 3 1 = 3 ln 2 81 728 - 117
S ECTION 9.1 D EFINITE I NTEGRALS 13. - 0 3 4 ) + ( dx x e x = 0 3 5 5 + - x e x = - - - 5 ) 3 ( + 5 0 + 5 3 5 0 e e = 3 5 248 - - e 14. 2 ln 0 x e dx = [ e x ] 2 ln 0 = e ln 2 e 0 = 1 15. dx e x - 1 0 4 = 1 0 4 4 1 - - x e = - - - - - ) 0 ( 4 ) 1 ( 4 4 1 4 1 e e = ) 1 ( 4 1 4 - - e 16. - 3 1 2 5 x e x dx = 3 1 2 2 1 ln 5 - x e x = - - - ) 1 ( 2 ) 3 ( 2 2 1 1 ln 5 2 1 3 ln 5 e e = ) ( 2 1 3 ln 5 2 6 e e - - 17. - - 4 4 2 5 dx e x = 4 4 2 5 5 2 - - - x e = - - - - - - 2 ) 4 ( 5 2 ) 4 ( 5 5 2 5 2 e e = ) ( 5 2 10 10 - - e e 18. - - - 2 2 3 3 ) ( x x e e dx = 2 2 3 3 3 1 3 1 - - + x x e e = + - + - - - - ) 2 ( 3 ) 2 ( 3 ) 2 ( 3 ) 2 ( 3 3 1 3 1 3 1 3 1 e e e e = 0 118

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CHAPTER 9 DEFINITE INTEGRATION 19. dx
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MS-Sol-EE-C09 - CHAPTER 9 DEFINITE INTEGRATION Section 9.1...

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