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Paul
August 7, 2018

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

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