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Calculus III (Assignment Problems) / Multiple Integrals / Double Integrals over General Regions   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Assignment Problems
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals
Iterated Integrals Previous Section   Next Section Double Integrals in Polar Coordinates

 Double Integrals Over General Regions

 

1. Evaluate  where   

 

2. Evaluate  where    

 

3. Evaluate  where D is the region in the 1st quadrant bounded by  and .

 

4. Evaluate  where D is the region bounded by  and .

 

5. Evaluate  where D is the region bounded by  and .

 

6. Evaluate  where D is the triangle with vertices ,  and .

 

7. Evaluate  where D is the region bounded by ,  and the x-axis.  

 

8. Evaluate  where D is the region in the 2nd quadrant bounded by ,  and the y-axis.

 

9. Evaluate  where D is the region shown below.

 

10. Evaluate  where D is the region shown below.

 

11. Evaluate  where D is the region shown below. 

 

12. Evaluate  where D is the region bounded by ,  and  in the order given below.

   (a) Integrate with respect to x first and then y.

   (b) Integrate with respect to y first and then x.

 

13. Evaluate  where D is the region bounded by ,  and  in the order given below.

   (a) Integrate with respect to x first and then y.

   (b) Integrate with respect to y first and then x.

 

For problems 14  16 evaluate the given integral by first reversing the order of integration.

 

14.    

 

15.    

 

16.   

 

17. Use a double integral to determine the area of the region bounded by  and .

 

18. Use a double integral to determine the area of the region bounded by  and .

 

19. Use a double integral to determine the volume of the region that is between the xy-plane and  and is above the region in the xy-plane that is bounded by  and .

 

20. Use a double integral to determine the volume of the region that is between the xy-plane and  and is above the region in the xy-plane that is bounded by ,  and the x-axis.

 

21. Use a double integral to determine the volume of the region in the first octant that is below the plane given by .

 

22. Use a double integral to determine the volume of the region bounded by , the surface  and the planes  and .

 

23. Use a double integral to determine the volume of the region bounded by the planes , ,  and .

 

24.  Use a double integral to determine the formula for the area of a right triangle with base, b and height h.

 

25.  Use a double integral to determine a formula for the figure below.

 

 

Iterated Integrals Previous Section   Next Section Double Integrals in Polar Coordinates
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals

Calculus III (Assignment Problems) / Multiple Integrals / Double Integrals over General Regions    [Notes] [Practice Problems] [Assignment Problems]

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