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Exercises. Double integrals

# Exercises. Double integrals - Exercises Double integrals...

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Exercises. Double integrals. Evaluate the following iterated integrals and sketch the region over which each integration takes place. 1. - 2 0 2 3 0 ) 4 ( dy y dx 2. - - + + 1 1 0 1 ) 1 ( dx y x dy 3. - - 0 2 2 3 0 ) 2 ( dy xy y x dx 4. + 1 0 2 2 0 ) 2 ( dx y x dy 5. + 2 1 2 4 3 ) ( y x dy dx 6. + + 2 1 2 3 0 ) 2 ( dx x y yx dy 7. + 1 0 2 2 0 ) 2 ( dx xy e x dy y 8. + 1 0 2 0 ) 3 sin ( dx y y x dy π 9. + x x y x dy e dx 2 2 ln 0 10. x x y dy x dx / 1 2 2 2 1 11. - - + 5 4 3 3 2 ) 2 ( y dx y x dy 12. a a rdr d ϕ sin 2 0

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13. - ϕ π cos 3 0 2 2 2 / 2 / sin dr r d 14. + 0 2 ) cos (sin dx x x dy 15. x ydy x dx 0 0 sin 16. + y y x dx e dy ln 0 8 ln 1 17. x ydy dx sin 0 0 18. 2 2 1 y y dx dy Evaluate the following integrals. 19. y xy dx ye dy / 1 0 1 10 20. 3 0 / 1 0 x x y dy e dx Double integrals. The double integral of a function
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Exercises. Double integrals - Exercises Double integrals...

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