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Author: Tinku Tara

0-1-e-r-2-sin-1-r-2-ln-r-1-r-2-dr-

Question Number 223580 by Nicholas666 last updated on 30/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}\:} \:\frac{{e}^{−\boldsymbol{{r}}^{\mathrm{2}} } \boldsymbol{\mathrm{sin}}\left(\mathrm{1}/\boldsymbol{{r}}^{\mathrm{2}} \right)\boldsymbol{\mathrm{ln}}\left(\boldsymbol{{r}}+\mathrm{1}\right)}{\boldsymbol{{r}}^{\mathrm{2}} }\:\boldsymbol{\mathrm{d}{r}} \\ $$$$ \\ $$ Answered by MathematicalUser2357…

Question-223585

Question Number 223585 by hardmath last updated on 30/Jul/25 Commented by hardmath last updated on 30/Jul/25 $$\mathrm{Radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:=\:\mathrm{R} \\ $$$$\mathrm{AB}\:\bot\:\mathrm{CD} \\ $$$$\mathrm{AC}\:=\:\mathrm{a} \\ $$$$\mathrm{BD}\:=\:\mathrm{b} \\ $$$$\mathrm{Prove}\:\mathrm{that}:\:\mathrm{R}\:=\:\frac{\sqrt{\mathrm{a}^{\mathrm{2}}…

S-1-1-1-2-2-3-3-16-16-S-2-1-1-2-2-3-3-14-14-Find-S-1-S-2-

Question Number 223571 by hardmath last updated on 30/Jul/25 $$\mathrm{S}_{\mathrm{1}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+…+\:\mathrm{16}\centerdot\mathrm{16}! \\ $$$$\mathrm{S}_{\mathrm{2}} \:=\:\mathrm{1}\centerdot\mathrm{1}!\:+\:\mathrm{2}\centerdot\mathrm{2}!\:+\:\mathrm{3}\centerdot\mathrm{3}!\:+…+\:\mathrm{14}\centerdot\mathrm{14}! \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{S}_{\mathrm{1}} }{\mathrm{S}_{\mathrm{2}} }\:=\:? \\ $$ Answered by parthasc last updated…

0-1-ln-x-x-ln-3-1-x-1-x-dx-

Question Number 223534 by Tawa11 last updated on 28/Jul/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{ln}^{\mathrm{3}} \left(\frac{\mathrm{1}\:\:−\:\:\mathrm{x}}{\mathrm{1}\:\:+\:\:\mathrm{x}}\right)\:\mathrm{dx} \\ $$ Answered by MathematicalUser2357 last updated on 31/Jul/25 $$\:\cancel{\:} \\ $$…

x-y-36-xy-max-

Question Number 223538 by fantastic last updated on 28/Jul/25 $${x}+{y}=\mathrm{36} \\ $$$${xy}_{{max}} =?? \\ $$ Answered by Frix last updated on 28/Jul/25 $$\mathrm{Max}\:\mathrm{at}\:{x}={y}=\mathrm{18}\:\mathrm{because}\:\mathrm{out}\:\mathrm{of}\:\mathrm{all}\:\mathrm{rectangles} \\ $$$$\mathrm{with}\:\mathrm{given}\:\mathrm{circumference}\:\mathrm{the}\:\mathrm{square}\:\mathrm{has}\:\mathrm{the}…