Question

b. Use the change of variables \( u=3 x+y, v=x+3 y \) to compute the integral \[ \iint_{R}(x+3 y) d A \] where \( R \) is the parallelogram enclosed by the lines \[ 3 x+y=9,3 x+y=33, x+3 y=3, x+3 y=27 \] [Its vertices are \( (0,9),(9,6),(12,-3) \) and \( (3,0) \). (10 marks)

          b. Use the change of variables \( u=3 x+y, v=x+3 y \) to compute the integral
\[
\iint_{R}(x+3 y) d A
\]
where \( R \) is the parallelogram enclosed by the lines
\[
3 x+y=9,3 x+y=33, x+3 y=3, x+3 y=27
\]
[Its vertices are \( (0,9),(9,6),(12,-3) \) and \( (3,0) \).
(10 marks)

b. Use the change of variables u=3 x+y, v=x+3 y to compute the integral

∬R(x+3 y) d A

where R is the parallelogram enclosed by the lines

3 x+y=9,3 x+y=33, x+3 y=3, x+3 y=27

[Its vertices are (0,9),(9,6),(12,-3) and (3,0).
(10 marks)

Added by Cynthia M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Leon Druch

Step 1

Given the change of variables \( u=3x+y \) and \( v=x+3y \), we can express the integral \( \iint_{R}(x+3y)dA \) in terms of \( u \) and \( v \). Since \( v=x+3y \), the integrand is simply \( v \). Show more…

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b. Use the change of variables \( u=3 x+y, v=x+3 y \) to compute the integral \[ \iint_{R}(x+3 y) d A \] where \( R \) is the parallelogram enclosed by the lines \[ 3 x+y=9,3 x+y=33, x+3 y=3, x+3 y=27 \] [Its vertices are \( (0,9),(9,6),(12,-3) \) and \( (3,0) \). (10 marks)