Consider the region R in the ry-plane bounded by the lines y = x, y = 2x, x+ y = 2. We make the following substitution u = y – x, v = y – 2x and we call S the image of R by this substitution. 1. Give a figure for R in the xy-plane and a figure for S in the uv-plane. 2. Evaluate the double integral || (x+y)dA. R

Consider the region R in the ry-plane bounded by the lines y = x, y = 2x, x+ y = 2. We make the following substitution u = y – x, v = y – 2x and we call S the image of R by this substitution. 1. Give a figure for R in the xy-plane and a figure for S in the uv-plane. 2. Evaluate the double integral || (x+y)dA. R

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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Question

Consider the region R in the xy-plane bounded by the lines y = x, y = 2x, x + y = 2.
We make the following substitution
u = y – x, v = y – 2x
and we call S the image of R by this substitution.
1. Give a figure for R in the xy-plane and a figure for S in the uv-plane.
2. Evaluate the double integral || (x+y)dA.
R

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