Question Number 20202 by Joel577 last updated on 24/Aug/17 $$\mathrm{Is}\:\mathrm{definite}\:\mathrm{integral}\:\mathrm{can}\:\mathrm{have}\:\mathrm{negative}\:\mathrm{value}? \\ $$$$\mathrm{Because}\:\mathrm{I}\:\mathrm{think}\:\int_{{a}} ^{{b}} {f}\left({x}\right)\:{dx}\:\mathrm{is}\:\mathrm{total}\:\mathrm{area}\:\mathrm{below} \\ $$$$\mathrm{graph}\:{f}\left({x}\right)\:\mathrm{from}\:{x}\:=\:{a}\:\mathrm{until}\:{x}\:=\:{b},\:\mathrm{so}\:\mathrm{it}\:\mathrm{can}'\mathrm{t} \\ $$$$\mathrm{be}\:\mathrm{negative} \\ $$ Commented by ajfour last updated…
Question Number 151268 by rs4089 last updated on 19/Aug/21 $$\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} }{{r}}\left[\psi\left(\frac{{r}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{4}}\right)−\psi\left(\frac{{r}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{4}}\right)\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85721 by M±th+et£s last updated on 24/Mar/20 $${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {ln}\left({x}\right)}{\:\sqrt{{x}}}{dx}=−\sqrt{\pi}\left(\gamma+{ln}\left(\mathrm{4}\right)\right) \\ $$ Answered by mind is power last updated on…
Question Number 85718 by M±th+et£s last updated on 24/Mar/20 $$\int\frac{{sin}\left({x}\right)−{cos}\left(\mathrm{3}{x}\right)}{{sin}\left({x}\right)−{cos}\left(\mathrm{2}{x}\right)}{dx} \\ $$ Answered by MJS last updated on 24/Mar/20 $$\int\frac{\mathrm{sin}\:{x}\:−\mathrm{cos}\:\mathrm{3}{x}}{\mathrm{sin}\:{x}\:−\mathrm{cos}\:\mathrm{2}{x}}{dx}= \\ $$$$=\int\frac{\mathrm{4cos}\:{x}\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}}{−\mathrm{2cos}^{\mathrm{2}} \:{x}\:+\mathrm{sin}\:{x}\:+\mathrm{1}}{dx}= \\…
Question Number 85717 by M±th+et£s last updated on 24/Mar/20 $$\int_{\mathrm{0}} ^{\mathrm{2}} {x}^{\mathrm{4}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{10}} \left(\mathrm{1}−{x}^{{n}} \right){dx} \\ $$$$ \\…
Question Number 85711 by Rio Michael last updated on 24/Mar/20 $$\:\underset{−\mathrm{4}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{2}{x}\:+\:\mathrm{1}}{\left({x}^{\mathrm{2}} +\:{x}\:+\:\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} }\:{dx} \\ $$ Commented by jagoll last updated on 24/Mar/20 $$\underset{−\mathrm{4}}…
Question Number 151246 by mathmax by abdo last updated on 19/Aug/21 $$\mathrm{find}\:\mathrm{I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{cosx}\right)\mathrm{dx}\:\mathrm{and}\:\mathrm{J}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{sinx}\right)\mathrm{dx} \\ $$ Answered by qaz last updated on 19/Aug/21…
Question Number 20166 by tammi last updated on 23/Aug/17 $$\int\mathrm{cosec}\:^{\mathrm{2}} {xdx} \\ $$ Answered by sma3l2996 last updated on 23/Aug/17 $${t}={cosecx}\Rightarrow{dt}=−\frac{{cosec}^{\mathrm{2}} {x}}{{secx}}{dx} \\ $$$${cosec}^{\mathrm{2}} {xdx}=−\frac{{tdt}}{\:\sqrt{{t}^{\mathrm{2}}…
Question Number 20167 by tammi last updated on 23/Aug/17 $${please}\:{solve}\:{it} \\ $$$${integrate}\:{with}\:{respect}\:{to}\:{x} \\ $$$$\int\frac{\mathrm{5}{x}−\mathrm{2}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}} \\ $$ Answered by ajfour last updated on 23/Aug/17 $$=\frac{\mathrm{1}}{\mathrm{3}}\int\frac{\left(\mathrm{5}/\mathrm{2}\right)\left(\mathrm{2}{x}+\mathrm{2}/\mathrm{3}\right)−\mathrm{11}/\mathrm{3}}{\left({x}+\mathrm{1}/\mathrm{3}\right)^{\mathrm{2}}…
Question Number 20164 by tammi last updated on 23/Aug/17 $$\int\frac{{e}^{\mathrm{tan}^{−\mathrm{1}} {x}} }{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$ Answered by ajfour last updated on 23/Aug/17 $${let}\:\mathrm{tan}^{−\mathrm{1}} {x}={t} \\…