Menu Close

Category: Integration

Question-123154

Question Number 123154 by liberty last updated on 23/Nov/20 Answered by benjo_mathlover last updated on 23/Nov/20 $$\:{let}\:{t}=\mathrm{sin}\:\:{q}\:\Rightarrow{dt}\:=\:\mathrm{cos}\:{q}\:{dq} \\ $$$$\eta\:\left({x}\right)=\:\int\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {q}}\:\left(\mathrm{cos}\:{q}\:{dq}\right) \\ $$$$\eta\:\left({x}\right)=\:\int\left(\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{q}}{\mathrm{2}}\right)\:{dq}\: \\ $$$$\eta\:\left({x}\right)=\:\frac{{q}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{q}}{\mathrm{2}}\:+\:{c}\: \\…

1-x-1-x-dx-

Question Number 123037 by benjo_mathlover last updated on 22/Nov/20 $$\:\:\int\:\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}\:{dx} \\ $$$$ \\ $$ Answered by MJS_new last updated on 22/Nov/20 $$\int\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\frac{\sqrt{\mathrm{1}−{x}}}{\mathrm{1}−\sqrt{{x}}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}\left(\mathrm{1}−\sqrt{{x}}\right)\sqrt{\mathrm{1}−{x}}\right] \\…

Question-123034

Question Number 123034 by benjo_mathlover last updated on 21/Nov/20 Answered by mathmax by abdo last updated on 21/Nov/20 $$\chi\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx}\:\:\Rightarrow\chi=_{\mathrm{x}=\frac{\mathrm{1}}{\mathrm{t}}} \:\:\:−\int_{\mathrm{0}} ^{\infty} \:\:\frac{−\mathrm{lnt}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{t}^{\mathrm{2}}…

1-findF-a-0-cos-ln-2-x-2-a-2-x-2-dx-witha-gt-0-2-find-the-value-of-0-cos-ln-2-x-2-4-x-2-dx-

Question Number 57490 by Abdo msup. last updated on 05/Apr/19 $$\left.\mathrm{1}\right){findF}\left({a}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx}\:\:{witha}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx}. \\ $$ Commented…

advanced-calculus-calculate-I-0-pi-x-1-sin-x-cos-x-dx-

Question Number 123023 by mnjuly1970 last updated on 21/Nov/20 $$\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{calculus}… \\ $$$${calculate}::: \\ $$$$\:\:\:\:\:\mathrm{I}:\overset{???} {=}\:\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\mathrm{1}−{sin}\left({x}\right){cos}\left({x}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………………….. \\ $$ Answered by mnjuly1970 last…