2014 - Math 6A Exam 4 (1).pdf - Name MATH 6A EXAM 4(100...

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Unformatted text preview: Name:_____________________________ MATH 6A: EXAM 4 (100 points) Time: 60 minutes Directions: Relative work must be shown in order to receive credit. Simplify all answers (no calculator approximations unless specified). Partial credit is rewarded, so it is to your benefit to show steps. Clearly label answers. If space provided is insufficient, additional scratch paper may be used. Be sure to clearly label the problems on any additional sheets used. Good luck! (1) Given the function f (x) = 2x 2 on [1,6] , find the right Riemann Sum using n = 5 partitions. 6 6 6 4 1 1 4 1 (2) Given the following definite integrals ∫ f (x)dx = 10 , ∫ g(x)dx = 5 , ∫ f (x)dx = 5 , and ∫ g(x)dx = 2 answer the following questions. 6 (a) ∫ ( f (x) − g(x)) dx = 1 1 (b) ∫ 3g(x)dx = 4 6 (c) ∫ ( g(x) − f (x)) dx = 4 (3) Find the net area of region bounded by f (x) = x(x − 2) and the x-­‐axis on the interval [0,5] . (4) Find the area of region bounded by f (x) = x(x − 2) and the x-­‐axis on the interval [0,5] . (5) The surface of a water wave is described by y = 5 (1+ cos x ) , for −π ≤ x ≤ π . Find the average height of the wave. (6) Given the velocity function v(t) = 6t 2 + 4t − 10 and s(0) = 3 , find the position function and the acceleration function. (7) Find the indefinite integral. ∫ ( ) x +1 2 x 4 dx (8) Find the indefinite integral. ∫ y dy ( y + 1)3 (9) Evaluate the integral. 4 ∫x 2 x 2 − 1 dx 1 (10) Evaluate the integral. π cos x dx 2 x ∫ sin π 2 4 ...
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