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If u_(n)=int_(0)^((pi)/(2))(sin(2n-1)x)/(sinx)dxandv_(n)=int_(0)^((pi)/(2))((sinnx)/(sinx))^(2)dx and n is an integer, prove that, u_(n+1)=u_(n)andv_(n+1)-v_(n)=u_(n+1). |
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