Let f : R" → R be defined by f(x1, x2, ... , xn) = x1X2•••Xn on the cube [0, 1] × [0, 1] × · · × [0,1] (i.e. for 0 < x1 < 1,0 < x2 < 1,...,0 < ¤n < 1). Evaluate 1 ,Xn) dx1 dx2 · dxn X2, · ... .. •1 1 Use your result to calculate X2, ·.., Txp Ixp ("x dxn .. ... n=0
Let f : R" → R be defined by f(x1, x2, ... , xn) = x1X2•••Xn on the cube [0, 1] × [0, 1] × · · × [0,1] (i.e. for 0 < x1 < 1,0 < x2 < 1,...,0 < ¤n < 1). Evaluate 1 ,Xn) dx1 dx2 · dxn X2, · ... .. •1 1 Use your result to calculate X2, ·.., Txp Ixp ("x dxn .. ... n=0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![4.
Let f : R" → R be defined by f(x1, x2,... , Xn)
= x1X2°
..· Xn on the cube
[0, 1] × [0, 1] × ·..
x [0, 1] (i.e. for 0 < x1 < 1,0 < x2 < 1,...,0 < xn < 1). Evaluate
1
,In) dx1 dx2
dan
..
..
1
Use your result to calculate
X2,
, Xn) dx1 dx2
dxn
n=0
5.
The average value favg of the function f : R? →R over the domain D is given
1
by the formula favg
= iD // f(r, y) dA, where m(D) is the measure of the size of
D (in general, this could be length, area, volume, etc.) Find the average value of the
function f(x, y) = x sin (xy) on the square [0, T] × [0, 7].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75f96cc1-f20f-41e8-af87-e67129ee7f4c%2F85f19938-721c-4126-b733-d0d38b70958f%2Fatxtna_processed.png&w=3840&q=75)
Transcribed Image Text:4.
Let f : R" → R be defined by f(x1, x2,... , Xn)
= x1X2°
..· Xn on the cube
[0, 1] × [0, 1] × ·..
x [0, 1] (i.e. for 0 < x1 < 1,0 < x2 < 1,...,0 < xn < 1). Evaluate
1
,In) dx1 dx2
dan
..
..
1
Use your result to calculate
X2,
, Xn) dx1 dx2
dxn
n=0
5.
The average value favg of the function f : R? →R over the domain D is given
1
by the formula favg
= iD // f(r, y) dA, where m(D) is the measure of the size of
D (in general, this could be length, area, volume, etc.) Find the average value of the
function f(x, y) = x sin (xy) on the square [0, T] × [0, 7].
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