Use the given transformation to evaluate the integral a) ff (x − 3y) dA where R is the triangular region with vertices (0,0), (2,1), and (1,2); R with x = 2u+v, y = u + 2v b) ff (x²) d4 where R is the region bounded by the ellipse 9x² + 4y² = 36 R with x = 2u, y = 3v

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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show full and complete procedure HANDWRITTEN only. please answer a) and b) as they are subparts of the same question 

Use the given transformation to evaluate the integral
a) ff (x
(x − 3y) dA where R is the triangular region with vertices (0,0), (2,1), and (1,2);
R
with x = 2u + v, y = u + 2v
b) ff (x²) dA where R is the region bounded by the ellipse 9x² + 4y² = 36
R
with x = 2u, y = 3v
Transcribed Image Text:Use the given transformation to evaluate the integral a) ff (x (x − 3y) dA where R is the triangular region with vertices (0,0), (2,1), and (1,2); R with x = 2u + v, y = u + 2v b) ff (x²) dA where R is the region bounded by the ellipse 9x² + 4y² = 36 R with x = 2u, y = 3v
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