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Category: Integration

J-0-1-1-x-4-dx-

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}}…

0-pi-2-sin-2-4-sin-2-d-

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-205361

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} \\…

3x-x-3-1-3-dx-

Question Number 205294 by depressiveshrek last updated on 15/Mar/24 $$\int\sqrt[{\mathrm{3}}]{\mathrm{3}{x}−{x}^{\mathrm{3}} }{dx} \\ $$ Answered by Frix last updated on 15/Mar/24 $$\int\left(\mathrm{3}{x}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx}\:\overset{{t}=\frac{{x}^{\mathrm{2}} }{\mathrm{3}}} {=}\:\frac{\mathrm{3}}{\mathrm{2}}\int{t}^{−\frac{\mathrm{1}}{\mathrm{3}}}…