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Calculus III (Practice Problems) / Multiple Integrals / Double Integrals in Polar Coordinates   [Notes] [Practice Problems] [Assignment Problems]

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

 

1. Evaluate  where D is the region in the 3rd quadrant between  and . [Solution]

 

2. Evaluate   where is the bottom half of . [Solution]

 

3. Evaluate  where D is the portion of  in the 1st quadrant. [Solution]

 

4. Use a double integral to determine the area of the region that is inside  and outside . [Solution] 

 

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

 

 

[Solution]

 

6. Use a double integral to determine the volume of the solid that is inside the cylinder , below  and above the xy-plane. [Solution]

 

7. Use a double integral to determine the volume of the solid that is bounded by  and . [Solution] 

 

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

Calculus III (Practice Problems) / Multiple Integrals / Double Integrals in Polar Coordinates    [Notes] [Practice Problems] [Assignment Problems]

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