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Calculus III (Practice Problems) / Multiple Integrals / Change of Variables   [Notes] [Practice Problems] [Assignment Problems]

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On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.

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Paul
August 7, 2018


Calculus III - Practice Problems
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals
Triple Integrals in Spherical Coordinates Previous Section   Next Section Surface Area

 

For problems 1  3 compute the Jacobian of each transformation.

 

1.   [Solution]

 

2.   [Solution]

 

3.   [Solution]

 

4. If R is the region inside  determine the region we would get applying the transformation ,  to R. [Solution]

 

5. If R is the parallelogram with vertices , ,  and  determine the region we would get applying the transformation ,  to R. [Solution]

 

6. If R is the region bounded by , ,  and  determine the region we would get applying the transformation ,  to R. [Solution]

 

7. Evaluate  where R is the region bounded by , ,  and  using the transformation , . [Solution]

 

8. Evaluate  where R is the parallelogram with vertices , ,  and  using the transformation ,  to R. [Solution]

 

9. Evaluate  where R is the triangle with vertices ,  and  using the transformation ,  to R. [Solution]

 

10. Derive the transformation used in problem 8. [Solution]

 

11. Derive a transformation that will convert the triangle with vertices ,  and  into a right triangle with the right angle occurring at the origin of the uv system. [Solution]

 

Problem Pane
Triple Integrals in Spherical Coordinates Previous Section   Next Section Surface Area
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals

Calculus III (Practice Problems) / Multiple Integrals / Change of Variables    [Notes] [Practice Problems] [Assignment Problems]

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