Category: Integration

Question Number 135174 by bemath last updated on 11/Mar/21 $$\mathcal{Z}\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \mathrm{arctan}\:\left(\mathrm{sin}\:\mathrm{x}\right)\:\mathrm{dx}\:+\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \mathrm{arcsin}\:\left(\mathrm{tan}\:\mathrm{x}\right)\:\mathrm{dx} \\ $$ Answered by john_santu last updated on 11/Mar/21 $${let}\:\mathcal{Z}_{\mathrm{1}} =\int_{\mathrm{0}}…

Question Number 69623 by aliesam last updated on 25/Sep/19 $$\int\frac{\mathrm{1}}{\:\sqrt{{x}}\:+\:\sqrt[{\mathrm{3}}]{{x}}}\:{dx} \\ $$ Answered by MJS last updated on 25/Sep/19 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{before}… \\ $$$$\int\frac{{dx}}{{x}^{\mathrm{1}/\mathrm{2}} +{x}^{\mathrm{1}/\mathrm{3}} }= \\…

Question Number 69597 by ozodbek last updated on 25/Sep/19 Commented by mathmax by abdo last updated on 25/Sep/19 $${generally}\:{let}\:{find}\:{f}\left({a}\right)\:=\int\sqrt{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$${changement}\:{x}\:={ash}\left({t}\right)\:{give}\:{f}\left({a}\right)=\int{ach}\left({t}\right){ach}\left({t}\right){dt} \\ $$$$={a}^{\mathrm{2}}…

Question Number 69573 by Ajao yinka last updated on 25/Sep/19 Commented by mind is power last updated on 25/Sep/19 $${i}\:{will}\:{try}\:{later}\:{now}\:{nothing}\:{goes}\:{wellfor}\:{this}\:{one} \\ $$ Terms of Service…

Question Number 69566 by Ajao yinka last updated on 25/Sep/19 Answered by mind is power last updated on 25/Sep/19 $$=\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\sum_{{k}=\mathrm{0}} ^{{x}} \int_{{k}} ^{{k}+\mathrm{1}} \left({x}−{k}\right)^{{k}}…