Category: Integration

Question Number 138428 by tugu last updated on 13/Apr/21 $$whattheareaofareaboundedbyline$$$$y=\mid lnx\mid andy=2$$ Answered by Ñï= last updated on 13/Apr/21 $$\mid lnx\mid =2$$$$\Rightarrow{x}={e}^{\mathrm{2}} ,{e}^{−\mathrm{2}}…

Question Number 72888 by mathmax by abdo last updated on 04/Nov/19 $$letf\left(x\right)={\int }_{\frac{\pi }{6}}^{\frac{\pi }{4}}\frac{tant}{2+xcost}dtwithxreal$$$$1)determineaexplicitformforf\left(x\right)$$$$2)determinealsog\left(x\right)={\int }_{\frac{\pi }{6}}^{\frac{\pi }{4}}\frac{tant}{{(2+xcost)}^2}dx$$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{tant}}{\left(\mathrm{2}+\mathrm{3}{cost}\right)}{dt}\:{and}\:\int_{\frac{\pi}{\mathrm{6}}}…

Question Number 138422 by mnjuly1970 last updated on 13/Apr/21 $$\dots \dots .nicecalculus\dots ..$$$$evaluate:$$$$\mathit{\varphi }={\int }_0^{\mathrm{\infty }}\frac{\sqrt[3]{1+x}-\sqrt[3]{x}}{\sqrt{x}}{}^{}dx=?$$$$$$ Terms of Service Privacy…

Question Number 138407 by tugu last updated on 13/Apr/21 $$iftheF\left(x\right)=\frac{1}{x}\underset{1}{\stackrel{x}{\int }}(2t-F{}^{\prime }\left(t\right))dt\Rightarrow whattheF{}^{\prime }\left(1\right)valueusingtheLeibnitzformula.$$ Answered by ajfour last updated on 13/Apr/21 $$F{}^{\prime }\left(x\right)=-\frac{F\left(x\right)}{x}+\frac{1}{x}[2x-F{}^{\prime }\left(x\right)]$$$$\left({x}+\mathrm{1}\right){F}\:'\left({x}\right)+{F}\left({x}\right)=\mathrm{2}{x} \…

Question Number 7300 by Tawakalitu. last updated on 22/Aug/16 $${\int }_0^{\frac{\mathrm{\Pi }}{2}}\frac{sinx}{sinx+cosx}dx$$ Answered by Yozzia last updated on 22/Aug/16 $${I}=\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{{sinx}}{{sinx}+{cosx}}{dx} \…