Summer (Session 1) 2006 - Mohanty's Class - Exam 2

Summer (Session 1) 2006 - Mohanty's Class - Exam 2 -...

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1 SOLUTION Midterm 2, Summer ’06, Math 20E Print name___________________________ ± Be sure to show your work. No credit will be given for unsupported answers. ± Please leave your arithmetic unfinished, unless the problem states otherwise. ± Look over the entire test first and start with the problems that look easiest. 1. (8 pts) Let be a continuous function on the solid W , which is bounded by planes ) , , ( z y x f , 0 , 1 = = y x 0 = z and 8 2 4 = + + z y x . Fill in the limits below, paying careful attention to the order of integration. 1 2 3 4 5 Total Out of 56 Solution: given the order of integration specified in the problem, the two outside limits need to cover the projection of W onto the xy -plane, which is the right triangle bounded by the x -axis, the line x =1, and the line shown shaded in the picture below. 4 2 = + y x 2 4 = + y x ∫∫∫ = W dV z y x f ) , , ( ∫∫ ∫ 2 1 2 4 0 2 4 8 0 ) , , ( x y x dx dy dz z y x f 1 z y 8 4 2 x
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2. (16 pts) Consider the integral , where D is the parallelogram bounded by the lines , , dy dx y x I D ∫∫ + = 3 0 3 = + y x 3 3 = + y x 0 = y x , and 1 =
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This note was uploaded on 04/30/2008 for the course MATH 20E taught by Professor Enright during the Summer '07 term at UCSD.

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Summer (Session 1) 2006 - Mohanty's Class - Exam 2 -...

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