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Category: Integration

1-pi-2-pi-3-1-sinx-cosx-dx-

Question Number 176570 by mathlove last updated on 21/Sep/22 $$\left(\mathrm{1}\right)\:\:\underset{\frac{\pi}{\mathrm{3}}} {\int}^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}+{sinx}}{{cosx}}\:{dx}=? \\ $$ Answered by Peace last updated on 21/Sep/22 $$\int\frac{\mathrm{1}+{sin}\left({x}\right)}{{cos}\left({x}\right)}{dx}=\int\frac{{cos}\left({x}\right)}{{cos}^{\mathrm{2}} \left({x}\right)}+\int\frac{{sin}\left({x}\right)}{{cos}\left({x}\right)}{dx} \\ $$$$=\int\frac{{cos}\left({x}\right)}{\mathrm{1}−{sin}^{\mathrm{2}}…

calculate-n-0-1-2n-1-e-4n-2-where-e-is-euler-number-solution-n-0-1-e-4n-2-0-1-x-2n-dx-

Question Number 176566 by mnjuly1970 last updated on 21/Sep/22 $$−−−− \\ $$$$\:\:{calculate}:\:\:\:\:\Phi\:=\:\underset{{n}=\mathrm{0}} {\overset{\:\infty} {\sum}}\:\frac{\:\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\:\right).{e}^{\:\mathrm{4}{n}+\mathrm{2}} }\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:{where}\:\:''\:\:{e}\:\:''\:\:{is}\:\:{euler}\:{number}. \\ $$$$\:\:\:\:\:\:\prec\:\:\:{solution}\:\:\succ \\ $$$$\:\:\:\:\:\:\Phi\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{e}^{\:\mathrm{4}{n}+\mathrm{2}} }\:\int_{\mathrm{0}} ^{\:\mathrm{1}}…

log-JS-farmer-1-tan-ln-x-tan-ln-x-2-dx-x-2-sin-cos-x-lt-cos-sin-x-where-0-x-2pi-

Question Number 111027 by john santu last updated on 01/Sep/20 $$\:\:\bigstar\frac{\mathrm{log}\:_{{JS}} \left({farmer}\right)}{}\bigstar \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{tan}\:\left(\mathrm{ln}\:{x}\right)\mathrm{tan}\:\left(\mathrm{ln}\:\left(\frac{{x}}{\mathrm{2}}\right)\right){dx}}{{x}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}\:\left(\mathrm{cos}\:{x}\right)\:<\:\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)\:;\:{where} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi \\ $$ Terms of Service Privacy Policy…

Question-45482

Question Number 45482 by Meritguide1234 last updated on 13/Oct/18 Answered by ajfour last updated on 13/Oct/18 $${f}\left({x}\right)=\frac{\mathrm{1}−\mathrm{2}{x}}{\mathrm{7}}\:\:;\:\:\:\:{f}\left(\mathrm{4}\right)=\:−\mathrm{1}\: \\ $$$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ $$$${let}\:\:\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}+\mathrm{1} \\ $$$$\int_{\mathrm{0}} ^{\:\:{x}}…

bemath-dx-4-3-2x-1-3-1-4-

Question Number 111017 by bemath last updated on 01/Sep/20 $$\:\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\int\:\frac{\mathrm{dx}}{\:\sqrt[{\mathrm{4}\:}]{\mathrm{4}−\sqrt[{\mathrm{3}\:}]{\mathrm{3}−\mathrm{2x}}}}\:? \\ $$ Answered by john santu last updated on 01/Sep/20 $${by}\:{letting}\:\nu\:=\:\sqrt[{\mathrm{4}\:}]{\mathrm{4}−\sqrt[{\mathrm{3}\:}]{\mathrm{3}−\mathrm{2}{x}}} \\ $$$$\Rightarrow\nu^{\mathrm{4}}…