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Paul
August 7, 2018

Calculus III - Assignment Problems
 Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals Double Integrals over General Regions Previous Section Next Section Triple Integrals

## Double Integrals in Polar Coordinates

1. Evaluate  where D is the unit circle centered at the origin.

2. Evaluate  where D is the top half of region between  and  .

3. Evaluate  where D is the portion of  in the 2nd quadrant.

4. Evaluate  where D is the region between  and

5. Evaluate  where D is the region in the 4th quadrant between  and .

6. Use a double integral to determine the area of the region that is inside .

7. Use a double integral to determine the area of the region that is inside  and outside .

8. Evaluate the following integral by first converting to an integral in polar coordinates.

9. Evaluate the following integral by first converting to an integral in polar coordinates.

10. Use a double integral to determine the volume of the solid that is below  and above the xy-plane.

11. Use a double integral to determine the volume of the solid that is bounded by  and .

12. Use a double integral to determine the volume of the solid that is inside both the cylinder  and the sphere .

13. Use a double integral to derive the area of a circle of radius a.

14. Use a double integral to derive the area of the region between circles of radius a and b with .  See the image below for a sketch of the region.

 Double Integrals over General Regions Previous Section Next Section Triple Integrals Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals

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