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Category: Integration

let-consider-the-function-f-x-x-x-2-ln-2-sin-cost-dt-calculate-f-x-x-and-f-x-

Question Number 32363 by prof Abdo imad last updated on 23/Mar/18 $${let}\:{consider}\:{the}\:{function} \\ $$$${f}\left({x},\theta\right)\:=\:\:\int_{{x}} ^{{x}^{\mathrm{2}} } {ln}\left(\:\mathrm{2}+{sin}\theta\:{cost}\right){dt} \\ $$$${calculate}\:\frac{\partial{f}}{\partial{x}}\left({x},\theta\right)\:{and}\:\:\frac{\partial{f}}{\partial\theta}\left({x},\theta\right)\:. \\ $$ Commented by prof Abdo…

Question-97892

Question Number 97892 by pranesh last updated on 10/Jun/20 Answered by john santu last updated on 10/Jun/20 $$\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x} \\ $$$$\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4x} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{8}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4x} \\…