MAT 1322 Study Guide - Final Guide: Limit Comparison Test, Exhaust Gas, Improper Integral
5 Mar 2015
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Total = 55: (5 marks) (a) (3 marks) find the value of the improper integral. 1 (b) (2 marks) use comparison test to show that the improper integral. 4 / 3 x x dx is divergent. Solution. (a) let u = - x3. (b) since 1 + sin2 x lim b. 10 m diverges: (5 marks) a conical tank has depth 8 meters and the radius of the top is 10 meters. It is filled with water of density r = 1000 kg / m3. Set up and evaluate an integral to compute the work, in. Joules, needed to pump the water to a point 2 meters above the ground level. (use g = 9. 8 m/sec2, p = 3. 14). Let h be the distance from a layer of water to the bottom of the cone. Then the radius of this layer r = (10 / 8)h = 5h / 4.
