Jacobian: Change of Variables Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the Jacobian of the change of variables and

(2) Find the Jacobian of the change of variables and

(3) Find the Jacobian of the change of variables and

(4) Find the Jacobian of the change of variables and

(5) Find the Jacobian of the change of variables and

(6) Find the Jacobian of the change of variables and

(7) Find the Jacobian given and

(8) Evaluate the double integral by using a change of variables, where is the region in the -plane bonded by the coordinate axes and the line

(9) Evaluate the double integral by using a change of variables, where is the region in the -plane bonded by the coordinate axes and the line   

(10) Evaluate the double integral by using a change of variables, where is the square in the -plane with vertices and

(11) Evaluate the double integral by using a change of variables, where is the square in the -plane with vertices and

(12) Evaluate the double integral by using a change of variables, where is the trapezoid with vertices and

(13) Let be the region in the -plane that is bounded by the coordinate axes and the line Use the change of variables to compute the integral  

(14) Under the change of variables the quarter circle region in the -plane given by is mapped onto a certain region of the -plane. Evaluate  

(15) Evaluate where is the region bounded by the parallelogram with vertices and

(16) A rotation of the -plane through the fixed angle is given by



Compute the Jacobian Let denote the region bounded by the ellipse Use a rotation of to obtain an integral that is equivalent to



Evaluate the transformed integral.

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Jacobians Change Of Variables Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/jacobians-change-of-variables-homework.html