232sampleexam1solution

# 232sampleexam1solution - MA 23200 NAME PUID Exam 1...

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MA 23200 NAME: Exam 1 PUID: INSTRUCTIONS No books or notes are allowed. You may use a one-line scientific calculator. No other electronic device is allowed. Be sure to turn off your cellphone. Show all your work in the space provided. Little or no credit may be given for an answer with insufficient or inconsistent work, even if the answer happens to be correct. Write answers in the boxes provided. All answers are expected to be simplified ( 2 4 1 2 , 2 x + x 3 x , e ln 2 2, etc). Question Possible Score 1 8 2 8 3 10 4 10 5 10 6 8 7 8 8 10 9 10 10 10 11 8 Total 100 The Trapezoid Rule for estimating the integral R b a f ( x ) dx with n trapezoids is given by T n = 1 2 Δ x [ f ( x 0 ) + 2 f ( x 1 ) + · · · + 2 f ( x n - 1 ) + f ( x n )] where Δ x = b - a n , x 0 = a , x 1 = a + Δ x , x 2 = a + 2Δ x , . . . , x n = a + n Δ x = b . 1

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For Problems 1 - 5, evaluate the given integrals. On the problems 1 through 3, use the substitution method. On problems 4 and 5, use integration by parts.
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