2220hw6 - Math 2220 Section 5.3 : Problem Set 6 Spring 2010...

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Unformatted text preview: Math 2220 Section 5.3 : Problem Set 6 Spring 2010 3 ex 6. Sketch the region of integration for the integral 0 1 2 dy dx , then reverse the order of integration and evaluate both integrals, the original one and the one with the order reversed. π /2 cos x 8. Do the same things for 1 sin x dy dx . 0 −x x2 −2 0 10. For the integral −2 (x − y ) dy dx reverse the order of integration to obtain a 1 x 2 2−x 0 sum of integrals, and evaluate the resulting integrals. 12. Reverse the order of integration in a single integral, and evaluate this integral. ππ sin x 16. Evaluate dx dy x 0y 2 1 y/2 0 0 sin x dy dx + 1 sin x dy dx to obtain 18. Evaluate 0 e−x dx dy 2 Section 5.4 : 2. Evaluate [0,1]×[0,2]×[0,3] (x2 + y 2 + z 2 ) dV 12. Integrate the function f (x, y, z ) = y over the region bounded by the plane x + y + z = 2 , the cylinder x2 + z 2 = 1 , and y = 0 . 14. Integrate f (x, y, z ) = z over the region in the first octant bounded by the cylinder y 2 + z 2 = 9 and the planes y = x , x = 0 , and z = 0 . 16. Integrate f (x, y, z ) = 3x over the region in the first octant bounded by z = x2 + y 2 , x = 0 , y = 0 , and z = 4 . 20. Find the volume of the region inside both the cylinders x2 + y 2 = a2 and x2 + z 2 = a2 . 1 1 0 0 36−4x2 −4y 2 5x2 x2 22. Change the order of integration of equivalent iterated integrals. 2 0 1 2 f (x, y, z ) dz dx dy to give five other √ 36−9x2 24. Consider the iterated integral 0 0 2 dz dy dx . (a) Describe the region of integration in R3 . (b) Set up an equivalent triple integral (c) Set up an equivalent triple integral 2 dz dx dy . Do not evaluate your answer. 2 dy dz dx . Do not evaluate your answer. ...
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