265Lesson14Problems

265Lesson14Problems - , 2] [0 , 4 ]. (5) Its a little messy...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 14 PROBLEMS Problems are worth 20 points each. (1) Compute the Riemann sum for ZZ R (2 x + 3 y ) d A where R = [1 , 5] × [2 , 4]. The rectangle R is partitioned by horizontal and vertical lines at the integers, and the sample points are the upper left corner of each subrectangle. (2) Evaluate the iterated integral Z 2 0 Z 3 2 xy 2 d x d y . (3) Evaluate the iterated integral Z π 4 0 Z π 2 0 sin x cos 2 y d x d y . (4) Convert the double integral to an iterated integral and evaluate ZZ W e x cos 2 y d A , where W = [1
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Unformatted text preview: , 2] [0 , 4 ]. (5) Its a little messy to compute Z 1 Z 1 x 1 + xy d x d y as written. But its much easier if the order of integration is reversed. So, apply Fubinis Theorem to reverse the order of integration, and evaluate the new iterated integral. (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Evaluate ZZ S ln x y d A , where S = [1 ,e ] [1 , 2 e ]. 1...
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