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1007_Test4_Sol

1007_Test4_Sol - MATH 1007 A Test#4 SOLUTIONS 1[2 marks Z 3...

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Unformatted text preview: MATH 1007 A Test #4 November 17, 2006 SOLUTIONS 1. [2 marks] Z 3 √ x 2 dx Solution: Z 3 √ x 2 dx = Z x 2 / 3 dx = 1 5 / 3 x 5 / 3 + C = 3 5 x 5 / 3 + C 2. [2 marks] Z e- x + sin x dx Solution: Z e- x + sin x dx =- e- x- cos x + C 3. [2 marks] Z 2 1 8 x 3- 9 x 2 dx Solution: Z 2 1 8 x 3- 9 x 2 dx = 8 · 1 4 x 4- 9 · 1 3 x 3 2 1 = 2 x 4- 3 x 3 2 1 = (2 · 2 4- 3 · 2 3 )- (2 · 1 4- 3 · 1 3 ) = (32- 24)- (- 1) = 9 1 4. [3 marks] Z 4 (1 + 2 x ) 3 dx Solution: Z 4 (1 + 2 x ) 3 dx = Z 2 (1 + 2 x ) 3 2 dx let u = 1 + 2 x, du = 2 dx = Z 2 u 3 du =- u- 2 + C =- (1 + 2 x )- 2 + C 5. [3 marks] Z x 3 √ 2 x 4- 1 dx Solution: Z x 3 √ 2 x 4- 1 dx = Z √ 2 x 4- 1 · 1 8 · 8 x 3 dx let u = 2 x 4- 1 , du = 8 x 3 dx = Z √ u · 1 8 du = 1 8 · 1 3 / 2 · u 3 / 2 + C = 1 12 · (2 x 4- 1) 3 / 2 + C 2 6. [3 marks] Z 1 5- x dx Solution: Z 1 5- x dx = Z- 1 5- x (- 1) dx let u = 5- x, du =- dx = Z- 1 u du =- ln | u | + C =- ln | 5- x | + C 7. [4 marks] Z 2 1 x 2- 4 x 3 dx Solution: Z 2 1 x 2- 4 x...
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1007_Test4_Sol - MATH 1007 A Test#4 SOLUTIONS 1[2 marks Z 3...

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