quiz4sol

quiz4sol - I = Z 1 x 2 dx respectively Circle the correct...

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Math 126 Calculus II (Fall 2006) Quiz 4 (10 pts) Name: Section (circle one): 8AM 9AM Instructions: Read each question carefully, clearly mark your answers, and remember to show your work . 1. (4 pts) Find the area of the region bounded by the curves y = 1 x , y = 1 x 2 , and x = 2. Solution: A = Z 2 1 ± 1 x - 1 x 2 ² dx = ³ ln x + 1 x ´ 2 1 = (ln 2 + 1 2 ) - (ln 1 + 1) = ln 2 - 1 2 . 2. (4 pts) Find the length of the curve y = Z x 1 p t - 1 dt , 1 x 16. Solution: y = Z x 1 p t - 1 dt dy dx = p x - 1 1 + ± dy dx ² 2 = 1 + ( x - 1) = x . Thus, L = Z 16 1 p xdx = Z 16 1 x 1 4 dx = 4 5 x 5 4 µ µ µ µ 16 1 = 4 5 (32 - 1) = 124 5 . 3. (2 pts) Let L 10 , R 10 , T 10 , M 10 , S 10 be the left endpoint, right endpoint, trapezoidal, midpoint, and Simpson’s approximations of
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Unformatted text preview: I = Z 1 x 2 dx , respectively. Circle the correct inequalities from the following (there may be more than one correct): (a) L 10 < I < R 10 (b) L 10 > I > R 10 (c) T 10 < M 10 (d) T 10 > M 10 (e) T 10 < I (f) T 10 > I (g) S 10 = I (h) S 10 < I . Solution: (a), (d), (f), (g). Sketch the graphs and we see directly that (a), (d), and (f) are true. Since x 2 is a polynomial of degree no more than three, (g) is true....
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This note was uploaded on 05/04/2008 for the course MATH 218 taught by Professor Haskell during the Fall '06 term at USC.

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