Question Number 179478 by Acem last updated on 29/Oct/22 $${Find}\:\int_{\:\mathrm{0}} ^{\:\frac{\mathrm{1}}{\mathrm{6}}} \:\frac{\mathrm{1}}{{x}^{−\mathrm{5}} \:\left(\mathrm{36}{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx} \\ $$ Answered by MJS_new last updated on 29/Oct/22 $$\int\frac{{dx}}{{x}^{−\mathrm{5}}…
Question Number 113929 by gloriousman last updated on 16/Sep/20 $$\int\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{5}} \mathrm{dx}\: \\ $$$$ \\ $$ Commented by ShakaLaka last updated on 16/Sep/20 $${we}\:{can}\:{also}\:{solve}\:{by}\:{simplification} \\…
Question Number 113910 by bobhans last updated on 16/Sep/20 $$\left(\mathrm{1}\right)\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{4}} {x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} }\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{{x}}\right)}}{\frac{\mathrm{1}}{{x}}}\:? \\ $$ Answered by bemath last updated on…
Question Number 113907 by bemath last updated on 16/Sep/20 $$\int\:\sqrt{{x}}\:\mathrm{cos}\:\left(\sqrt{{x}}\right)\:{dx} \\ $$ Answered by bobhans last updated on 16/Sep/20 $${K}=\int\:\sqrt{{x}}\:\mathrm{cos}\:\left(\sqrt{{x}}\right)\:{dx}\: \\ $$$${let}\:{x}={t}^{\mathrm{2}} \:\Rightarrow{dx}\:=\:\mathrm{2}{t}\:{dt}\: \\ $$$${K}=\:\int\:\mathrm{2}{t}^{\mathrm{2}}…
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Question Number 179405 by Acem last updated on 29/Oct/22 $$\:{Evaluate}\:\int\:\frac{{dx}}{{x}^{\mathrm{4}} \:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }} \\ $$ Answered by greougoury555 last updated on 29/Oct/22 $$\:{M}=\int\:\frac{{dx}}{{x}^{\mathrm{3}} \:{x}^{\mathrm{2}} \:\sqrt{\frac{\mathrm{9}}{{x}^{\mathrm{2}} }−\mathrm{1}}}\:{dx}…
Question Number 113867 by Ar Brandon last updated on 15/Sep/20 $$\int_{\mathrm{3}} ^{\mathrm{6}} \frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{6x}}\mathrm{dx} \\ $$ Answered by abdomsup last updated on 15/Sep/20 $${I}\:=\int_{\mathrm{3}}…
Question Number 113868 by Ar Brandon last updated on 15/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{between}\:\mathrm{the}\:\mathrm{circle}\:\rho=\mathrm{2acos}\theta\:\mathrm{and}\: \\ $$$$\mathrm{cardiode}\:\rho=\mathrm{a}\left(\mathrm{1}+\mathrm{cos}\theta\right) \\ $$ Commented by kaivan.ahmadi last updated on 18/Sep/20 $$\mathrm{2}{acos}\theta={a}+{acos}\theta\Rightarrow{acos}\theta={a}\Rightarrow{cos}\theta=\mathrm{1}\Rightarrow \\ $$$$\theta=\mathrm{0},\theta=\mathrm{2}\pi…
Question Number 113865 by Ar Brandon last updated on 15/Sep/20 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{series}\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{x}\left(\mathrm{lnx}\right)^{\mathrm{n}} \mathrm{dx}\:\mathrm{and}\:\mathrm{I}_{\mathrm{0}} =\int_{\mathrm{1}} ^{\mathrm{e}} \mathrm{xdx} \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{true}\:? \\ $$$$\mathrm{a}\backslash\:\mathrm{0}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\frac{\mathrm{e}^{\mathrm{2}} }{\mathrm{n}+\mathrm{2}}\:\:\:\:\mathrm{b}\backslash\mathrm{1}\leqslant\mathrm{I}_{\mathrm{n}} \leqslant\frac{\mathrm{e}^{\mathrm{2}}…
Question Number 179383 by Acem last updated on 29/Oct/22 $$\mathrm{1}\bullet\:{Evaluate}\:{I}=\int\:\:\frac{\sqrt{\mathrm{25}{x}^{\mathrm{2}} −\mathrm{4}}}{{x}}\:{dx} \\ $$$$\:\mathrm{2}\bullet\:{Find}\:{value}\:{of}\:\int_{\frac{\mathrm{2}}{\mathrm{5}}} ^{\:\frac{\mathrm{4}}{\mathrm{5}}} {f}\left({x}\right)\:{dx} \\ $$$$\:\mathrm{3}\bullet\:{Find}\:{value}\:{of}\:\int_{−\:\frac{\mathrm{4}}{\mathrm{5}}} ^{\:−\:\frac{\mathrm{2}}{\mathrm{5}}} {f}\left({x}\right)\:{dx} \\ $$$$ \\ $$ Answered by…