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Unformatted text preview: Reem Najjar Section Homework Set Homework1 due 04/07/2010 at 11:55pm EDT This set covers sections 5.15.3 of the text. You may need to give 4 or 5 significant digits for some (floating point) numerical answers in order to have them accepted by the computer. 1. (1 pt) Find the area of the inscribed polygon. 1 2 x 6 6 y y = 6 3 x 2 + 2 6 x + 2 2 Area = Correct Answers: • 6 2. (1 pt) The function f ( x ) = x 2 6 + 3 x is given over the inter val [ 2 , 2 ] . The interval is divided into 8 equal subintervals, x i is the mid point. Calculate the Riemann sum R P = ∑ n i = 1 f ( x i ) Δ x i . Answer: R P = Solution: R p = 8 ∑ i = 1 f ( x i ) Δ x i = 8 ∑ i = 1 f ( x i ) . 5 = . 5 ( f ( 1 . 75 )+ f ( 1 . 25 )+ f ( . 75 )+ ··· + f ( 1 . 75 )) = Correct Answers: • 0.875 3. (1 pt) Approximate the definite integral Z 8 4  5 t  dt using midpoint Riemann sums with the following partitions of the interval [ 4 , 8 ] : (a) Partititioning into two nonequal subintervals [ 4 , 5 ] and [ 5 , 8 ] . Then the midpoint Riemann sum = (b) Using 4 subintervals of equal length. Then the midpoint Riemann sum = Correct Answers: • 5 • 5 4. (1 pt) 18 ∑ n = ( 1 ) n 2 n = . Correct Answers: • 18 5. (1 pt) Write the sum using sigma notation: 1 1 · 2 + 1 2 · 3 + 1 3 · 4 + ··· + 1 104 · 105 = A ∑ n = 1 B , where A = and B = ....
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This note was uploaded on 10/25/2010 for the course MATH 152 taught by Professor Kurt during the Spring '08 term at Ohio State.
 Spring '08
 kurt
 Calculus

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