Question Number 85534 by liki last updated on 22/Mar/20 Commented by liki last updated on 22/Mar/20 $$….{please}\:{help}\:{idea}\:{question}\:{no}\:\mathrm{14}\left({a}\right) \\ $$ Commented by liki last updated on…
Question Number 151068 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\int_{\mathrm{0}} ^{\infty} \frac{\sqrt{\mathrm{x}}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{14x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{5}}{\mathrm{4}}} }\mathrm{dx}=\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85535 by liki last updated on 22/Mar/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85532 by oustmuchiya@gmail.com last updated on 22/Mar/20 $${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$ Answered by mind is power last updated on 22/Mar/20 $$\left(\mathrm{2}{a}−\frac{\mathrm{1}}{\mathrm{2}{a}}\right)^{{k}} \\ $$$$=\underset{{i}=\mathrm{0}} {\overset{{k}}…
Question Number 151070 by mathdanisur last updated on 18/Aug/21 $$\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{30}\:\:\:\mathrm{and}\:\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:+\:\frac{\mathrm{1}}{\mathrm{c}} \\ $$ Commented by john_santu last updated on 18/Aug/21 $$\frac{\mathrm{1}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}+\frac{\mathrm{1}}{\mathrm{c}}\geqslant\frac{\left(\mathrm{1}+\mathrm{1}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}=\frac{\mathrm{9}}{\mathrm{30}}=\frac{\mathrm{3}}{\mathrm{10}}…
Question Number 151065 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:\:::\:\:\int_{−\infty} ^{+\infty} \frac{\Gamma\left(\mathrm{x}\right)}{\Gamma\left(\mathrm{x}+\mathrm{a}\right)}\mathrm{sin}\:\left(\pi\mathrm{x}\right)\mathrm{dx}=\frac{\mathrm{2}^{\mathrm{a}−\mathrm{1}} }{\Gamma\left(\mathrm{a}\right)}\pi\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{a}>\mathrm{0}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151064 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\pi} \mathrm{arctan}\left(\frac{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{1}−\mathrm{2}\sqrt{\mathrm{2}}\varphi\mathrm{cos}\:\mathrm{x}+\mathrm{2}\varphi^{\mathrm{2}} }\right)\mathrm{dx}=\pi\mathrm{arctan}\:\sqrt{\varphi}\:\:\:\:\:\:\:\:\:\:\left(\varphi=\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151067 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\pi} \mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}\centerdot\mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{sin}\:\mathrm{x}}−\mathrm{1}\right)\mathrm{dx}=\sqrt{\mathrm{2}}\mathrm{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)+\left(\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right)\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151066 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\mathrm{arctan}\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{2}}\right)+\mathrm{arctan}\left(\frac{\mathrm{cos}\:\mathrm{3x}+\mathrm{15cos}\:\mathrm{x}}{\mathrm{8}}\right)\right)\mathrm{dx} \\ $$$$=\frac{\pi^{\mathrm{2}} }{\mathrm{4}}−\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151061 by qaz last updated on 18/Aug/21 $$\mathrm{Calculate}\:\:::\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{x}\centerdot\mathrm{cot}\:\mathrm{x}\centerdot\mathrm{ln}^{\mathrm{2}} \mathrm{cos}\:\mathrm{xdx}=\frac{\pi^{\mathrm{3}} }{\mathrm{24}}\mathrm{ln2}+\frac{\pi}{\mathrm{6}}\mathrm{ln}^{\mathrm{3}} \mathrm{2}−\frac{\mathrm{3}}{\mathrm{16}}\pi\zeta\left(\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com