Transforming a double integral to obtain constant limits Sometimes a multiple integral with variable limits can be changed into one with constant limits. By changing the order of integra- tion, show that f(x) g(x – y)f(y) dy) dx f(y) 8(x — у)fa) dx ) dy EL g( x – y|)f(x)f(y) dx dy.

Transforming a double integral to obtain constant limits Sometimes a multiple integral with variable limits can be changed into one with constant limits. By changing the order of integra- tion, show that f(x) g(x – y)f(y) dy) dx f(y) 8(x — у)fa) dx ) dy EL g( x – y|)f(x)f(y) dx dy.

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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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

Transforming a double integral to obtain constant limits
Sometimes a multiple integral with variable limits can be changed
into one with constant limits. By changing the order of integra-
tion, show that
f(x)
g(x – y)f(y) dy ) dx
f(y
g(x – y)f(x) dx ) dy
1| 8( \x – y }f(x)f(y) dx dy.

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