Question Number 139548 by peter frank last updated on 28/Apr/21 Answered by Dwaipayan Shikari last updated on 28/Apr/21 $$\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}} {sin}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{6}} }{dx}=−\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}}…
Question Number 74015 by mathmax by abdo last updated on 17/Nov/19 $${let}\:{f}\left({x}\right)\:=\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\:\frac{{sh}\left({xt}\right)}{{sin}\left({xt}\right)}{dt} \\ $$$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} {f}\left({x}\right) \\ $$ Commented by mathmax by abdo…
Question Number 74013 by mathmax by abdo last updated on 17/Nov/19 $${let}\:\:\:{P}\left({x}\right)=\:\sum_{\mathrm{0}\leqslant{i}<{j}\leqslant{n}} \:{x}^{{i}+{j}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{P}\:^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{P}\left({x}\right){dx} \\ $$ Commented by abdomathmax…
Question Number 139545 by aliibrahim1 last updated on 28/Apr/21 Answered by mr W last updated on 28/Apr/21 Commented by mr W last updated on 28/Apr/21…
Question Number 139544 by melanie last updated on 28/Apr/21 Answered by bemath last updated on 28/Apr/21 $$\:\mathrm{Tanzalin}\:\mathrm{formula} \\ $$$$\:\begin{array}{|c|c|c|c|}{\mathrm{u}\left(\mathrm{diff}\right)}&\hline{\mathrm{dv}\:\left(\mathrm{integrate}\right)}\\{\mathrm{4x}}&\hline{\mathrm{cos}\:\left(\mathrm{2}−\mathrm{3x}\right)}\\{\mathrm{4}}&\hline{−\frac{\mathrm{1}}{\mathrm{3}}\mathrm{sin}\:\left(\mathrm{2}−\mathrm{3x}\right)}\\{\mathrm{0}}&\hline{−\frac{\mathrm{1}}{\mathrm{9}}\mathrm{cos}\:\left(\mathrm{2}−\mathrm{3x}\right)}\\\hline\end{array} \\ $$$$\mathrm{I}=\:−\frac{\mathrm{4x}\:\mathrm{sin}\:\left(\mathrm{2}−\mathrm{3x}\right)}{\mathrm{3}}\:+\frac{\mathrm{4}\:\mathrm{cos}\:\left(\mathrm{2}−\mathrm{3x}\right)}{\mathrm{9}}\:+\:\mathrm{c}\: \\ $$ Answered by…
Question Number 74006 by necxxx last updated on 17/Nov/19 $${If}\:\mathrm{3}{x}^{\mathrm{2}} {e}^{\mathrm{log}\:_{{x}} \mathrm{27}} =\mathrm{27000}\:{then}\:{find}\:{x} \\ $$ Commented by necxxx last updated on 17/Nov/19 $${please}\:{how}\:{can}\:{this}\:{be}\:{solved}\:{analytically} \\ $$$${or}\:{even}\:{by}\:{numerical}\:{methods}=…
Question Number 8471 by PradipGos. last updated on 12/Oct/16 $$\underset{−\infty} {\overset{\infty} {\int}}{e}^{−\mathrm{2}\mid{x}\mid{d}\underset{} {{x}}} \:\:\:\:\:\:?\:\: \\ $$ Commented by FilupSmith last updated on 12/Oct/16 $$\mathrm{Do}\:\mathrm{you}\:\mathrm{mean}: \\…
Question Number 74005 by mhmd last updated on 17/Nov/19 $${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$ Terms of Service…
Question Number 8468 by FilupSmith last updated on 12/Oct/16 $$\mathrm{Prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that}: \\ $$$$\left(\mathrm{2}{k}+\mathrm{1}\right)^{{n}} \in\mathbb{O}\:\:\:\:\:\:\forall{k},{n}\in\mathbb{Z} \\ $$ Answered by Rasheed Soomro last updated on 12/Oct/16 $$\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{n}} =\begin{pmatrix}{\mathrm{n}}\\{\mathrm{0}}\end{pmatrix}\left(\mathrm{2k}\right)^{\mathrm{n}}…
Question Number 74003 by mhmd last updated on 17/Nov/19 $${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$ Commented by mr…