Consider the change of coordinates x=u2−v2, y=2uv. 1. (a) What is the Jacob

iohanetc

iohanetc

Answered question

2021-10-22

Consider the change of coordinates x=u2−v2, y=2uv.
1. (a) What is the Jacobian of this transformation?
2. (b) Let R be the image of the unit square [0, 1] × [0, 1] under this transformation. What is R? Describe it as a set and also plot a graph.
3.(c) Calculate the double integral over R
x2+y2dA
where here R is the region described by the previous part.

Answer & Explanation

SchepperJ

SchepperJ

Skilled2021-10-23Added 96 answers

Step 1
Hey, since there are multiple questions posted, we will answer first question. If you want any specific question to be answered then please submit that question only or specify the question number in your message.
1.(a) It is given that x=u2v2,y=2uv
Step 2
The Jacobian of this transformation is given below:
Jac=2u2vvu
=(2u)u-(2v(v))
=4u2+4v2

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