Question Number 134660 by benjo_mathlover last updated on 06/Mar/21 $$\mathscr{M}\:=\:\int\:\frac{{dx}}{\mathrm{2cos}\:{x}+\mathrm{3sin}\:{x}}\: \\ $$ Answered by EDWIN88 last updated on 06/Mar/21 $$\mathrm{Let}\:\begin{cases}{\mathrm{2}\:=\:\mathrm{r}\:\mathrm{sin}\:\alpha}\\{\mathrm{3}\:=\:\mathrm{r}\:\mathrm{cos}\:\alpha}\end{cases}\:\Rightarrow\:\mathrm{r}^{\mathrm{2}} =\:\mathrm{13};\:\mathrm{r}\:=\sqrt{\mathrm{13}} \\ $$$$\:\mathrm{and}\:\mathrm{tan}\:\alpha\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:,\therefore\:\alpha\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right) \\…
Question Number 134662 by mnjuly1970 last updated on 06/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:{calculus}… \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\boldsymbol{\phi}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\zeta\left(\mathrm{2}{n}\right)}{\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:…{m}.{n}… \\ $$ Answered by Dwaipayan Shikari last…
Question Number 3588 by prakash jain last updated on 16/Dec/15 $$\mathrm{Three}\:\mathrm{point}\:\mathrm{are}\:\mathrm{drawn}\:\mathrm{on}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{number}\:\mathrm{line}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}. \\ $$$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{quadractic}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} +{ax}+{b}=\mathrm{0} \\ $$$${a}=\mathrm{Length}\:\mathrm{of}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{AB} \\ $$$${b}=\mathrm{Length}\:\mathrm{of}\:\mathrm{line}\:\mathrm{segment}\:\mathrm{BC} \\ $$$$\mathrm{Give}\:\mathrm{construction}\:\mathrm{steps}\:\mathrm{to}\:\mathrm{identify}\:\mathrm{a}\:\mathrm{points} \\…
Question Number 134657 by Dwaipayan Shikari last updated on 06/Mar/21 $$\frac{\mathrm{1}}{\pi{e}}+\frac{\mathrm{3}}{\mathrm{2}\pi^{\mathrm{2}} {e}^{\mathrm{2}} }+\frac{\mathrm{11}}{\mathrm{6}\pi^{\mathrm{3}} {e}^{\mathrm{3}} }+\frac{\mathrm{25}}{\mathrm{12}\pi^{\mathrm{4}} {e}^{\mathrm{4}} }+\frac{\mathrm{137}}{\mathrm{60}\pi^{\mathrm{5}} {e}^{\mathrm{5}} }+…=\frac{{log}\left(\pi\right)+\mathrm{1}−{log}\left(\pi{e}−\mathrm{1}\right)}{\pi{e}−\mathrm{1}} \\ $$ Terms of Service Privacy…
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Question Number 69123 by TawaTawa last updated on 20/Sep/19 Answered by mr W last updated on 20/Sep/19 Commented by mr W last updated on 20/Sep/19…
Question Number 3584 by prakash jain last updated on 16/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\:\mathrm{pentagon}\:\mathrm{diagonal} \\ $$$$\mathrm{to}\:\mathrm{its}\:\mathrm{side}\:\mathrm{is}\:\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}. \\ $$ Commented by Yozzii last updated on 15/Dec/15 $${Its}\:{side}\:{is}\:{one}\:{of}\:{the}\:\mathrm{5}\:\:{edges}? \\ $$$$\:\:\:\:\:\:\:\:\:\:{a}\:\:\:\:\:\:\:\:{b}…
Question Number 69116 by ~ À ® @ 237 ~ last updated on 20/Sep/19 $$\:{Here}\:\:{are}\:{three}\:{propositions}:\: \\ $$$$−\:{This}\:{sentence}\:{has}\:{exactly}\:{six}\:{words} \\ $$$$−{There}\:{are}\:{two}\:{wrong}\:{propositions} \\ $$$$−{The}\:{two}\:{previous}\:{sentences}\:{are}\:{correct} \\ $$$$ \\ $$$${Among}\:{that}\:{propositions}\:,{how}\:{many}\:{are}\:{wrong}?\:{list}\:{them}!…
Question Number 134651 by 0731619177 last updated on 06/Mar/21 Answered by Ar Brandon last updated on 06/Mar/21 $$\mathrm{sinx}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\mathrm{x}^{\mathrm{2n}+\mathrm{1}} }{\left(\mathrm{2n}+\mathrm{1}\right)!}\:\Rightarrow\mathrm{sin}\pi\mathrm{x}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \frac{\left(\pi\mathrm{x}\right)^{\mathrm{2n}+\mathrm{1}}…
Question Number 69110 by Fawole last updated on 20/Sep/19 $${Evaluate}\:\int_{−\infty} ^{\infty} \frac{{cos}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Commented by mathmax by abdo last updated on 20/Sep/19 $$\:\:{let}\:{I}\:=\int_{−\infty}…