Question Number 212341 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{\mathrm{sin}\:{x}\:+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{5}}\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\right] \\ $$$$=−\frac{\mathrm{1}}{\mathrm{20}}\underset{\mathrm{0}} {\overset{\mathrm{4}/\mathrm{5}} {\int}}\frac{{dt}}{{t}^{\mathrm{2}}…
Question Number 212325 by MASANJAJJ last updated on 10/Oct/24 $${show}\:{that}\:\mathrm{1}+\sqrt{\mathrm{2}\:}+\mathrm{2}+……….+\mathrm{32}\sqrt{\mathrm{2}\:}\:{is}\:\mathrm{63}\sqrt{\mathrm{2}}\:+\mathrm{63} \\ $$ Answered by Ghisom last updated on 10/Oct/24 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{a}^{{k}} =\frac{{a}^{{n}+\mathrm{1}} −\mathrm{1}}{{a}−\mathrm{1}} \\…
Question Number 212342 by hardmath last updated on 10/Oct/24 $$\mathrm{The}\:\mathrm{number}\:\:\overline {\mathrm{abc}}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\overline {\mathrm{bca}}\:+\:\overline {\mathrm{cab}}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}.\: \\ $$ Answered by A5T last updated on 10/Oct/24 $$\mathrm{100}{a}+\mathrm{10}{b}+{c}\equiv−\mathrm{11}{a}−\mathrm{27}{b}+{c}=−\left(\mathrm{11}{a}+\mathrm{27}{b}−{c}\right)…
Question Number 212326 by universe last updated on 10/Oct/24 $$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{3}\right)^{{n}} \:{n}!}{\mathrm{1}.\mathrm{4}…\left(\mathrm{3}{n}+\mathrm{1}\right)} \\ $$$$\:\left(\mathrm{1}\right)\:{check}\:\:{its}\:{a}\:{absolute}\:{conergent}\:{series} \\ $$$$\:\:\left(\mathrm{2}\right)\:{show}\:{that}\:{its}\:{a}\:{convergent}\:{series} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 212327 by MASANJAJJ last updated on 10/Oct/24 $${if}\:\left({a}+\frac{\mathrm{1}}{{a}}\right)=\mathrm{15}\:{find}\:{the}\:{value}\:{of}\:\left({a}^{\mathrm{2}} \:+\frac{\mathrm{1}}{{a}^{\mathrm{2}} }\right) \\ $$ Answered by universe last updated on 10/Oct/24 $$\left({a}+\frac{\mathrm{1}}{{a}}\right)^{\mathrm{2}} \:=\:\mathrm{15}^{\mathrm{2}} \\ $$$${a}^{\mathrm{2}}…
Question Number 212320 by RojaTaniya last updated on 10/Oct/24 $$\:{a}+{b}+{c}+{d}=\mathrm{2},\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} =\mathrm{2} \\ $$$$\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} +{d}^{\mathrm{3}} =−\mathrm{4},\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} =−\mathrm{6} \\…
Question Number 212339 by Spillover last updated on 10/Oct/24 Answered by Ghisom last updated on 10/Oct/24 $$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\:\frac{{x}^{\mathrm{3}/\mathrm{4}} \left(\mathrm{3}−{x}\right)^{\mathrm{1}/\mathrm{4}} }{\left(\mathrm{5}−{x}\right)^{\mathrm{3}} }{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\left(\frac{\mathrm{2}{x}}{\mathrm{5}\left(\mathrm{3}−{x}\right)}\right)^{\mathrm{1}/\mathrm{4}} ;\:{C}=\frac{\mathrm{9}\sqrt[{\mathrm{4}}]{\mathrm{2}}}{\mathrm{5}\sqrt[{\mathrm{4}}]{\mathrm{5}}}\right]…
Question Number 212301 by RojaTaniya last updated on 09/Oct/24 $$\:\:\:\:\mathrm{3}{x}+\frac{\mathrm{2}}{\:\sqrt{{x}}}=\mathrm{1},\:{x}−\sqrt{{x}}\:=? \\ $$$$\:\: \\ $$ Answered by Sutrisno last updated on 09/Oct/24 $${misal}\:\sqrt{{x}}={p}\rightarrow{x}={p}^{\mathrm{2}} \\ $$$$\mathrm{3}{p}^{\mathrm{2}} +\frac{\mathrm{2}}{{p}}=\mathrm{1}…
Question Number 212319 by Ghisom last updated on 09/Oct/24 $$\mathrm{find} \\ $$$${G}=\frac{\mathrm{1}}{\mathrm{4}}\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}\:{dx} \\ $$ Commented by Spillover last updated on 10/Oct/24 $$\frac{\pi}{\mathrm{4}}\mathrm{ln}\:\mathrm{2}\:\:{right}? \\…
Question Number 212314 by Spillover last updated on 09/Oct/24 Answered by mehdee7396 last updated on 09/Oct/24 $${f}\left({x}\right)={ln}\left(\frac{\mathrm{2}−{sinx}}{\mathrm{2}+{sinx}}\right) \\ $$$${f}\left(−{x}\right)={ln}\left(\frac{\mathrm{2}+{sinx}}{\mathrm{2}−{sinx}}\right)=−{f}\left({x}\right) \\ $$$$\Rightarrow;{f};\:{is}\:\:;{odd}\Rightarrow\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} {f}\left({x}\right){dx}=\mathrm{0}\:\checkmark \\ $$$$…