Prove-0-pi-2-ln-sin-x-ln-cos-x-dx-pi-2-ln-2-2-pi-2-24-

Tinku Tara June 3, 2023 None 0 Comments

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Question Number 134613 by Ñï= last updated on 05/Mar/21

Prove::∫_0 ^(π/2) ln(sin x)ln(cos x)dx=(π/2)(ln^2 2−(π^2 /(24)))

P r o v e :: \int_{0}^{π / 2} l n (s i n x) l n (c o s x) d x = \frac{π}{2} ({l n}^{2} 2 - \frac{π^{2}}{24})

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