2220hw5 - Math 2220 Section 5.1 Problem Set 5 Spring 2010...

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Unformatted text preview: Math 2220 Section 5.1 : Problem Set 5 Spring 2010 √ ln x dx dy . 6. Evaluate the integral xy 11 8. Find the volume of the region bounded on the top by the plane z = x + 3y + 1 , on the 9 e bottom by the xy -plane, and on the sides by the planes x = 0 , x = 3 , y = 1 , y = 2 . For the following two problems, calculate the integral and indicate what region in R3 the integral is computing the volume of. 2 3 10. 0 3 1 2 dx dy . 1 0 14. −2 |x| sin πy dy dx . Section 5.2 : In the following two problems evaluate the integral and sketch the region in the xy -plane determined by the limits of integration. 2 x2 0 1 4. 0 y dy dx . √2 1−y 8. −1 0 3 dx dy . 12. Integrate the function f (x, y ) = 3xy over the region bounded by y = 32x3 and √ y = x. 14. Evaluate y = 3. 16. Evaluate D D 3y dA where D is the region bounded by xy 2 = 1 , y = x , x = 0 and (x2 + y 2 ) dA where D is the region in the first quadrant bounded by y = x , y = 3x , and xy = 3 . 28. (a) Show that if R = [a, b] × [c, d] , f is continuous on [a, b] , and g is continuous on b d [c, d] , then f (x)g (y ) dA = R a f (x) dx c g (y ) dy (b) What can you say about D f (x)g (y ) dA if D is not a rectangle? Specifically, what if D is an elementary region of type 1? ...
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This note was uploaded on 04/21/2010 for the course MATH 2220 taught by Professor Parkinson during the Spring '08 term at Cornell.

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