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

Calculus III - Assignment Problems
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Triple Integrals in Spherical Coordinates Previous Section   Next Section Surface Area

 Change of Variables

 

For problems 1  4 compute the Jacobian of each transformation.

 

1.   

 

2.   

 

3.   

 

4.   

 

5. If R is the region inside  determine the region we would get applying the transformation ,  to R.

 

6. If R is the triangle with vertices ,  and  determine the region we would get applying the transformation ,  to R.

 

7. If R is the parallelogram with vertices , ,  and  determine the region we would get applying the transformation ,  to R.

 

8. If R is the square defined by  and  determine the region we would get applying the transformation ,  to R.

 

9. If R is the parallelogram with vertices , ,  and  determine the region we would get applying the transformation ,  to R.

 

10. If R is the region bounded by , ,  and  determine the region we would get applying the transformation ,  to R.  

 

11. Evaluate  where R is the region bounded by , ,  and  using the transformation , .

 

12. Evaluate  where R is the triangle with vertices ,  and  using the transformation ,  to R.

 

13. Evaluate  where R is the parallelogram with vertices , ,  and  using the transformation ,  to R.

 

14. Evaluate  where R is the region bounded by , ,  and  using the transformation , .  

 

15. Evaluate  where R is the parallelogram with vertices , ,  and  using the transformation ,  to R.  

 

16. Derive a transformation that will transform the ellipse  into a unit circle.

 

17. Derive the transformation used in problem 12.

 

18. Derive the transformation used in problem 13.

 

19. Derive a transformation that will convert the parallelogram with vertices , ,  and  into a rectangle in the uv system.

 

20. Derive a transformation that will convert the parallelogram with vertices , ,  and  into a rectangle with one corner occurring at the origin of the uv system.

 

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

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

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