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YZ

# \begin{array}{c}\quad\quad\quad\quad{\text { a. Find the Jacobian of the transformation } x=u, y=u v \text { and }} \\ {\text { sketch the region } G : 1 \leq u \leq 2,1 \leq u v \leq 2, \text { in the }} \\ {\text { uv-plane. }} \\ {\text { b. Then use Equation }(2) \text { to transform the integral }} \\ {\int_{1}^{2} \int_{1}^{2} \frac{y}{x} d y d x}\end{array}

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### Video Transcript

first we need to fund the Jacoby in for that's six white over that if you re so, the Jacoby in J equals to 10 The You which issue in the region G will be sketched. See, it's basically to line into and fibula. We have new vehicles to, and you re close one. A unique Holt's one U equals two. That's the reason in for the integral we had when there were 21 over 13 to 1 to two x over. Boy, you would Yes, we know that exits one will transform too. You was to one and excuse to issue equals two. Why was one equals two You be used. One white was too too. Plus, you'd be wise to two. So over on our you and me playing the integral will be setting up as 1 to 21 over you two to over you You be Devi, do you And the answer for this will be equals two three over to some special off too. And if we value it's excellent. Why directive? Lee, We have 12 to 12 To what extent? What? E x first integrating with Mrs Kawai organ and 43 over two times, 1 to 2 yes or axe. So this is also through or two times natural, too. The two result. The two methods spring about the same result.

YZ
University of Illinois at Urbana-Champaign

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Limits

Integrals

Multiple Integrals

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