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Calculus III (Assignment Problems) / Multiple Integrals / Triple Integrals in Spherical Coordinates   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Assignment Problems

 Triple Integrals in Spherical Coordinates

 

1. Evaluate  where E is the sphere .

 

2. Evaluate  where E is the region between the spheres  and  with .

 

3. Evaluate  where E is the region below  and inside  that is in the 1st octant.

 

4. Evaluate  where E is the region between the spheres  and  and inside .

 

5. Evaluate  where E is the portion of  with .

 

6. Evaluate  where E is the region between the spheres  and  with  and  .

 

7. Evaluate the following integral by first converting to an integral in cylindrical coordinates.

 

 

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

 

 

9. Use a triple integral in spherical coordinates to derive the volume of a sphere with radius a.

 


Calculus III (Assignment Problems) / Multiple Integrals / Triple Integrals in Spherical Coordinates    [Notes] [Practice Problems] [Assignment Problems]

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