Question Number 2089 by Yozzi last updated on 01/Nov/15 $${If}\:{x}\in\left[\mathrm{0},\mathrm{0}.\mathrm{5}\pi\right],\:{show}\:{that}\:{sinx}\geqslant{x}−\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} . \\ $$$${Hence}\:{prove}\:{that} \\ $$$$\frac{\mathrm{1}}{\mathrm{3000}}\leqslant\int_{\mathrm{0}} ^{\mathrm{1}/\mathrm{10}} \frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}+{sinx}\right)^{\mathrm{2}} }{dx}\leqslant\frac{\mathrm{2}}{\mathrm{5999}}. \\ $$ Commented by prakash jain…
Question Number 67617 by aliesam last updated on 29/Aug/19 Commented by kaivan.ahmadi last updated on 29/Aug/19 $$\int\frac{\sqrt[{\mathrm{4}}]{{x}^{\mathrm{2}} −\mathrm{2}\sqrt[{\mathrm{4}}]{{x}^{\mathrm{6}} }+{x}}}{\:\sqrt[{\mathrm{4}}]{{x}^{\mathrm{3}} }}{dx}=\int\left(\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}}}−\mathrm{2}\sqrt[{\mathrm{4}}]{{x}^{\mathrm{3}} }+\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{x}^{\mathrm{2}} }}\right){dx}= \\ $$$$\int\left({x}^{\frac{−\mathrm{1}}{\mathrm{4}}} −\mathrm{2}{x}^{\frac{\mathrm{3}}{\mathrm{4}}}…
Question Number 67618 by mhmd last updated on 29/Aug/19 $${find}\:{the}\:{area}\:{abovnded}\:{r}={cos}\mathrm{2}\theta \\ $$ Answered by mr W last updated on 29/Aug/19 $${A}=\mathrm{8}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{r}^{\mathrm{2}} {d}\theta}{\mathrm{2}} \\…
Question Number 2069 by Yozzi last updated on 01/Nov/15 $${Find}\:{the}\:{integral} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\left({xcosh}\left({lnx}\right)\right)^{{n}} {dx} \\ $$$${where}\:{n}=\mathrm{0},\mathrm{1},\mathrm{2},… \\ $$ Commented by prakash jain last updated on 01/Nov/15…
Question Number 133125 by abdomsup last updated on 19/Feb/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cosx}\:{ch}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} \:+{x}+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last updated on 20/Feb/21…
Question Number 133124 by abdomsup last updated on 19/Feb/21 $${find}\:\int\:\:\frac{{dx}}{\left({x}+\mathrm{2}\right)^{\mathrm{2}} \left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133120 by abdomsup last updated on 19/Feb/21 $${calculate}\:{A}_{{n}} =\:\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.} \:\:\frac{{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } }{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{3}}}{dxdy} \\ $$$${and}\:{lim}_{{n}\rightarrow\infty} {A}_{{n}} \\ $$ Terms of Service…
Question Number 133121 by abdomsup last updated on 19/Feb/21 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{\:\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \left({n}+\rightarrow\infty\right) \\ $$ Answered by mindispower last updated on 19/Feb/21…
Question Number 133123 by abdomsup last updated on 19/Feb/21 $${find}\:\int\:\:\frac{{x}^{\mathrm{2}} {dx}}{{x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}} \\ $$ Answered by Ñï= last updated on 19/Feb/21 $$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{3}} −\mathrm{2}{x}+\mathrm{1}}{dx} \\…
Question Number 133119 by abdomsup last updated on 19/Feb/21 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{4}\right)^{\mathrm{3}} }{dx} \\ $$ Answered by mindispower last updated on 19/Feb/21 $${let} \\…