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Use the transformation x=u²-v², y = 2uv to evaluate the integral 2√1-1 ² √² + y² dy dz Hint: Show that the image of the triangular region G with vertices (0,0), (1,0), (1,1) in the uv-plane is the region of integration R in the xy-plane defined by the limits of integration.

Use the transformation x=u²-v², y = 2uv to evaluate the integral 2√1-1 ² √² + y² dy dz Hint: Show that the image of the triangular region G with vertices (0,0), (1,0), (1,1) in the uv-plane is the region of integration R in the xy-plane defined by the limits of integration.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) Use the transformation x = u²-v², y = 2uv to evaluate the integral 2√1- ¹²V¹=² √/x² + y² dy dx 6². Hint: Show that the image of the triangular region G with vertices (0,0), (1,0), (1,1) in the uv-plane is the region of integration R in the xy-plane defined by the limits of integration.
Transcribed Image Text:b) Use the transformation x = u²-v², y = 2uv to evaluate the integral 2√1- ¹²V¹=² √/x² + y² dy dx 6². Hint: Show that the image of the triangular region G with vertices (0,0), (1,0), (1,1) in the uv-plane is the region of integration R in the xy-plane defined by the limits of integration.
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