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2224Test2Review - MATH 2224: PRACTICE PROBLEMS FOR TEST #2...

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MATH 2224: PRACTICE PROBLEMS FOR TEST #2 1. Evaluate the following: a. dx dy x 1 0 x 3 0 2 ! ! b. ! ! " 2 0 y sin 0 x dy dx y cos e c. dy dx y 25 x 2 4 0 y 0 2 ! ! # d. ! ! ! # # # 6 0 x 6 0 z x 6 0 dx dz dy x 2. Reverse the order of integration and evaluate: ! ! + + 3 / 1 0 2 1 x 3 dx dy ) 3 x ( 3. Convert to rectangular coordinates and evaluate: ! ! " " $ # $ $ 3 4 4 3 sec 5 0 2 3 d dr sin r 4. Find the area of the region bounded by the graphs of 1 y x 2 2 = + , 9 y x 2 2 = + using iterated integrals in polar coordinates. 5. Convert to polar coordinates and evaluate: dx dy y x 3 3 x 9 0 2 2 2 ! ! # # + 6. Graph the bounded region in the xy-plane and evaluate the integral ! ! ! # # # # 1 1 x 1 x 1 5 0 2 2 dx dy dz . 7. Find the volume of the region bounded by the graphs of 2 y x = , 2 y x 4 = # , z = 0, and z = 3. 8. Set up the triple integral in cylindrical coordinates to find the volume under 0 z y x = # + above the region in the fourth quadrant that lies outside r = 1 and inside $ # = sin 1 r . Shade the proper region on the graph
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This note was uploaded on 04/05/2008 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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2224Test2Review - MATH 2224: PRACTICE PROBLEMS FOR TEST #2...

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