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1b-2008-exam_1

# 1b-2008-exam_1 - I using Simpson’s rule with n = 4(c Find...

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Name: Last, First Math 1B — Exam 1 Fall Program for Freshmen 2008 Fred Bourgoin You have 80 minutes to answer all questions. You may use a scientiﬁc calculator but not a graphing calculator. Show all your steps. Partial credit will be awarded if and when deserved. 1. (8 points) Find the area of the region bounded by y = sin x, y = sin 3 x, x = 0 , x = π 2 . 1

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2. (10 points) Evaluate Z 2 3 0 x 3 16 - x 2 dx . 3. (12 points) Evaluate Z 3 0 dx x 2 - x - 2 . 2
4. (20 points) Consider the integral I = Z 4 2 x dx . (a) Approximate I using the trapezoidal rule with n = 5. (b) Approximate

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Unformatted text preview: I using Simpson’s rule with n = 4. (c) Find upper bounds for both approximations. 3 5. (10 points) Compute Z dx √ 9 x 2 + 6 x-8 . 6. (10 points) Compute Z x 3-4 x-10 x 2-x-6 dx . 4 7. (10 points) Compute Z t 3 e 2 t dt . 8. (10 points) Evaluate Z te √ t dt . 5 9. (10 points) Evaluate the integral, or show that it diverges. Z ∞-∞ dx 4 x 2 + 4 x + 5 Extra Credit. Show that Z ∞ ln x 1 + x 2 dx = 0. 6...
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1b-2008-exam_1 - I using Simpson’s rule with n = 4(c Find...

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