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[Notes]
Calculus III - Practice 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   [Solution]

2. Evaluate  where D is the region bounded by  and . [Solution]

3. Evaluate  where D is the region bounded by  and . [Solution]

4. Evaluate  where D is the region bounded by  and . [Solution]

5. Evaluate  where D is the region bounded by ,  and the y-axis. [Solution]

6. Evaluate  where D is the region bounded by ,  and the x-axis. [Solution]

7. Evaluate  where D is the region shown below.

[Solution]

8. Evaluate  where D is the region shown below.

[Solution]

9. 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.

[Solution]

For problems 10 & 11 evaluate the given integral by first reversing the order of integration.

10.    [Solution]

11.    [Solution]

12. Use a double integral to determine the area of the region bounded by  and . [Solution]

13. Use a double integral to determine the volume of the region that is between the xy-plane and  and is above the triangle with vertices ,  and . [Solution]

14. Use a double integral to determine the volume of the region bounded by  and the planes , ,  and the xy-plane. [Solution]

15. Use a double integral to determine the volume of the region formed by the intersection of the two cylinders  and . [Solution]

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

[Notes]

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