homework2 - 2 2[10 points(5.5 79 It looks as if we can...

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Math 1120 Homework2 Due 9/8 or 9/9,2011 Name: GRADES Book questions / 8 Presentation questions / 30 Print out these pages. Answer the “presentation questions” in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these prob- lems. Writeyouranswerstothe“bookquestions”onseparate paper and staple to these pages. They will be assessed only for completeness. Always write neatly and legibly. Book questions — 5.5: 14, 36, 50, 60 5.6: 6a, 56, 84, 115 Presentation questions 1. [10 points] Evaluate integraldisplay 2 / 2 0 x 3 1 - x 2 dx . CONTINUE TO THE NEXT PAGE.
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Math 1120, Fall 2011 Homework 2 — due 9/8 or 9/9 2 2. [10 points] (5.5: 79) It looks as if we can integrate 2 sin
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Unformatted text preview: 2 2. [10 points] (5.5: 79) It looks as if we can integrate 2 sin x cos x with respect to x in three diFerent ways: a. i 2 sin x cos x dx = i 2 u du = u 2 + C 1 = sin 2 x + C 1 , where u = sin x . b. i 2 sin x cos x dx = i-2 u du =-u 2 + C 2 =-cos 2 x + C 2 , where u = cos x . c. i 2 sin x cos x dx = i sin 2 x dx =-cos 2 x 2 + C 3 . Can all three integrations be correct? Explain. CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 2 — due 9/8 or 9/9 3 3. [10 points] (5.6: 106) Find the area of the region in the ±rst quadrant bounded on the left by the y –axis, below by the curve x = 2 √ y , above left by the curve x = ( y-1) 2 , and above right by the line x = 3-y . THIS IS THE LAST PAGE....
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