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Category: Integration

show-that-the-improper-integral-lim-B-0-B-sin-x-sin-x-2-dx-converges-

Question Number 150994 by talminator2856791 last updated on 17/Aug/21 $$\: \\ $$$$\:\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{improper}\:\mathrm{integral} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\underset{{B}\rightarrow\infty} {\mathrm{lim}}\:\:\int_{\mathrm{0}} ^{\:{B}} \:\mathrm{sin}\left({x}\right)\mathrm{sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$\:\: \\ $$$$\:\:\:\mathrm{converges} \\…

6x-4-4-x-4-2-dx-

Question Number 85441 by jagoll last updated on 22/Mar/20 $$\int\:\frac{\mathrm{6x}^{\mathrm{4}} −\mathrm{4}}{\:\sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last updated on 22/Mar/20 $${I}\:=\:\int\:\frac{\mathrm{4}{x}^{\mathrm{4}} }{\:\sqrt{{x}^{\mathrm{4}} −\mathrm{2}}}\:{dx}\:=\:\mathrm{4}\int\:{x}\:\left(\frac{{x}^{\mathrm{3}}…