If D = [-1, 1] × [−1, 4], show the following. dx dy 5 ≤ 16 x² + x1/2² +1 - + ≤ 10
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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![If D = [-1, 1] x [-1, 4], show the following.
//
dx dy
x² + y² + 1
5
9
we know
VI
The area of the region D is given by
Then since 1 ≤ x² + y² + 1 ≤ 18 for all (x, y) E D,
1
+ y² + 1
10
Now integrating over D we have
]) = //
≤
< 10
dx dy
D x² + y² + 1
≤ 10.
S
dx dy
X x² + y² + 1
and finally dividing through by the area we obtain
1/3 ≤ 166 x ²2 + X
VI
for all (x, y) ED.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2F31e7ddc0-a4be-4cb4-82e0-6a9c95971c5f%2Fe1h34_processed.png&w=3840&q=75)
Transcribed Image Text:If D = [-1, 1] x [-1, 4], show the following.
//
dx dy
x² + y² + 1
5
9
we know
VI
The area of the region D is given by
Then since 1 ≤ x² + y² + 1 ≤ 18 for all (x, y) E D,
1
+ y² + 1
10
Now integrating over D we have
]) = //
≤
< 10
dx dy
D x² + y² + 1
≤ 10.
S
dx dy
X x² + y² + 1
and finally dividing through by the area we obtain
1/3 ≤ 166 x ²2 + X
VI
for all (x, y) ED.
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