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)!

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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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)!
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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