Let B be the unit box with corner at the origin of R³ given by B = [0, 1] × [0, 1] × [0, 1] × [0, 1] × [0, 1] (sometimes written B = [I-,[0, 1]). If ƒ(x) = 3201X2X3X4X5, compute i=1 integral ///|| f(x) dx (Note: Throughout this problem, x = the value of the (x1, X2, X3, X4, X5) and dx = dx1 dx2 dx3 dx4 dx5)
Let B be the unit box with corner at the origin of R³ given by B = [0, 1] × [0, 1] × [0, 1] × [0, 1] × [0, 1] (sometimes written B = [I-,[0, 1]). If ƒ(x) = 3201X2X3X4X5, compute i=1 integral ///|| f(x) dx (Note: Throughout this problem, x = the value of the (x1, X2, X3, X4, X5) and dx = dx1 dx2 dx3 dx4 dx5)
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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4. Please give detail as much as possible.
![Let \( B \) be the unit box with corner at the origin of \( \mathbb{R}^5 \) given by \( B = [0, 1] \times [0, 1] \times [0, 1] \times [0, 1] \times [0, 1] \) (sometimes written \( B = \prod_{i=1}^5 [0, 1] \)). If \( f(\mathbf{x}) = 32x_1x_2x_3x_4x_5 \), compute the value of the integral
\[
\int \int \int \int \int_B f(\mathbf{x}) \, d\mathbf{x}
\]
(Note: Throughout this problem, \( \mathbf{x} = (x_1, x_2, x_3, x_4, x_5) \) and \( d\mathbf{x} = dx_1 \, dx_2 \, dx_3 \, dx_4 \, dx_5 \)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaa0f822-544e-4e71-bb85-904850361648%2F56c7ea58-4507-4b29-8b57-6425d4b97480%2Fwwthmk_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( B \) be the unit box with corner at the origin of \( \mathbb{R}^5 \) given by \( B = [0, 1] \times [0, 1] \times [0, 1] \times [0, 1] \times [0, 1] \) (sometimes written \( B = \prod_{i=1}^5 [0, 1] \)). If \( f(\mathbf{x}) = 32x_1x_2x_3x_4x_5 \), compute the value of the integral
\[
\int \int \int \int \int_B f(\mathbf{x}) \, d\mathbf{x}
\]
(Note: Throughout this problem, \( \mathbf{x} = (x_1, x_2, x_3, x_4, x_5) \) and \( d\mathbf{x} = dx_1 \, dx_2 \, dx_3 \, dx_4 \, dx_5 \)).
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