3. Explain what is wrong with the following statement: If R is the region 0≤x≤ 1,0 ≤ y ≤ 4 and T is the region 0≤ s≤ 1,-2 ≤ t ≤ 2, using a = s, y = t2, we have f(x, y)dady = [ f(s, SR R t²) |(x, y) | a(s, t) dsdt

3. Explain what is wrong with the following statement: If R is the region 0≤x≤ 1,0 ≤ y ≤ 4 and T is the region 0≤ s≤ 1,-2 ≤ t ≤ 2, using a = s, y = t2, we have f(x, y)dady = [ f(s, SR R t²) |(x, y) | a(s, t) dsdt

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

3. Explain what is wrong with the following statement:
If R is the region 0 ≤ x ≤ 1,0 ≤ y ≤ 4 and T is the region 0 ≤ s≤ 1, -2 ≤ t ≤ 2,
using x = s, y = t2, we have
[ f(x, y)dady = ff(s, 1²)
R
(x, y)
a(s, t)
dsdt

Expert Solution

Step 1

To Examine: What is wrong with the following statement:

If R is the region $0 \leq x \leq 1, 0 \leq y \leq 4$ and $T$ is the region $0 \leq s \leq 1, - 2 \leq t \leq 2,$ using $x = s, y = t^{2}$ , we have

$\int_{R} f (x, y) d x d y = \int_{T} f (s, t^{2}) |\frac{\partial (x, y)}{\partial (s, t)}| d s d t$ .

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