Question Number 205873 by universe last updated on 01/Apr/24 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{\pi^{\mathrm{2}} }\:\frac{{x}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{3}} {x}\:}}\left[\left(\mathrm{3}\pi\mathrm{cos}{x}+\mathrm{4sin}{x}\right)\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{4}\right]{dx}\:\:\: \\ $$ Answered by Berbere last updated on 02/Apr/24 $${x}\rightarrow\pi−{x};{let}\:\Omega={integral}…
Question Number 205826 by tri26112004 last updated on 31/Mar/24 $$\underset{\left[\mathrm{0};\mathrm{3}\right]} {{f}}\left({x}\right)>\mathrm{0} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{8} \\ $$$$\underset{\mathrm{0}} {\int}^{\mathrm{3}} \frac{\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{{f}\left({x}\right)+\mathrm{1}}{dx}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$${f}\left(\mathrm{2}\right)=¿ \\ $$ Terms…
Question Number 205750 by MetaLahor1999 last updated on 29/Mar/24 $$\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{2}{x}} }{dx}=? \\ $$ Commented by mokys last updated on 29/Mar/24 $$=\:−\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\:\infty} \:\frac{−\mathrm{2}{e}^{−\mathrm{2}{x}}…
Question Number 205725 by NasaSara last updated on 28/Mar/24 Answered by Berbere last updated on 29/Mar/24 $$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}} \left[{xy}\right]{dydx}\overset{{xy}={t}} {=}\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}{x}}…
Question Number 205599 by mnjuly1970 last updated on 25/Mar/24 $$ \\ $$$$\:{laplace}\:{transform}… \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\mathscr{L}\:\left\{\:\:{sin}\left(\sqrt{{t}}\:\right)\right\}\:=? \\ $$$$−−−− \\ $$ Commented by SANOGO last updated…
Question Number 205625 by Lindemann last updated on 25/Mar/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Answered by mathzup last updated on 25/Mar/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{4}}…
Question Number 205590 by Lindemann last updated on 25/Mar/24 $${J}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Commented by lepuissantcedricjunior last updated on 25/Mar/24 $$\boldsymbol{{J}}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−\boldsymbol{{x}}^{\mathrm{4}}…
Question Number 205558 by universe last updated on 24/Mar/24 $$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \:\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{4}\theta\:}{\mathrm{sin}^{\mathrm{2}} \theta\:}{d}\theta\:\:=\:\:\:? \\ $$ Answered by Berbere last updated on 24/Mar/24 $${sin}^{\mathrm{2}} \left(\mathrm{4}{x}\right)=\mathrm{4}{sin}^{\mathrm{2}}…
Question Number 205506 by Lindemann last updated on 23/Mar/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{4}} }{dx} \\ $$ Answered by sniper237 last updated on 23/Mar/24 $$\overset{{u}={x}^{\mathrm{4}} } {=}\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}}…
Question Number 205361 by Lambertician last updated on 18/Mar/24 Answered by Berbere last updated on 18/Mar/24 $$=−\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{xln}\left(\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}\right)}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}−\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\boldsymbol{{x}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}} \\ $$$$=−\mathrm{4}{a}−{q} \\…