Prove the irrationality of n² by expressing the integral In - = 6.² P(x) sin x dx as a linear combination of 1, ², 4, ..., n2n over Z, where 1 P(x) = x²n (π- x)²n (2n)!
Prove the irrationality of n² by expressing the integral In - = 6.² P(x) sin x dx as a linear combination of 1, ², 4, ..., n2n over Z, where 1 P(x) = x²n (π- x)²n (2n)!
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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Transcribed Image Text:Prove the irrationality of n² by expressing the integral
In =
= ["
P(x) sin x dx
0
as a linear combination of 1, ², ², ..., ²n over Z, where
1
P(x) = x²n(π - x)²n
(2n)!
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