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Question Number 105706 by bramlex last updated on 31/Jul/20
∫π0dx(5−cosx)3?
Answered by john santu last updated on 31/Jul/20
F(a)=∫π0dxa−cosx=πa2−1F′(a)=∫∂∂a[dxa−cosx]=∂∂a[πa2−1]−∫π0(dx(a−cosx)2)=−πa2(a2−1)−3/2F″(a)=∫π0∂∂a[dx(a−cosx)2]=−π[(a2−1)−3/2−3a2(a2−1)−5/2]∫π0dx(1−cosx)3=−π2(a2−1)−5/2((a2−1)−3a2)=π2.2a2+1(a2−1)5/2puta=5∫π0dx(5−cosx)3=11π64.★
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