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Category: Integration

0-pi-4-sin-x-sin-x-cos-x-dx-

Question Number 127528 by bramlexs22 last updated on 30/Dec/20 $$\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}\:\mathrm{dx}\:=?\: \\ $$ Answered by liberty last updated on 30/Dec/20 $$\:{Let}\:{L}\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{4}} \frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:{dx}\: \\…

let-f-x-0-1-ln-1-xt-3-dt-with-x-lt-1-1-find-a-explicit-form-of-f-x-2-calculate-0-1-ln-1-1-2-t-3-dt-3-calculate-A-0-1-ln-1-sin-t-3-dt-with-0-lt-lt-pi-2-

Question Number 61978 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{xt}^{\mathrm{3}} \right){dt}\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}{t}^{\mathrm{3}} \right){dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{A}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}}…

let-A-n-1-n-n-arctan-x-2-y-2-x-2-y-2-dxdy-1-calculate-A-n-2-find-lim-n-A-n-

Question Number 61976 by maxmathsup by imad last updated on 13/Jun/19 $${let}\:{A}_{{n}} =\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} \:\:\:\frac{{arctan}\left({x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:{dxdy}\:\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{A}_{{n}} \\…

if-f-x-x-16-x-2-3-find-0-5-3-5-f-x-dx-using-trapezoidal-method-then-find-the-max-and-min-value-of-the-error-with-the-given-n-steps-x-n-f-x-n-

Question Number 193036 by ali009 last updated on 02/Jun/23 $${if}\:{f}\left({x}\right)={x}\sqrt{\left(\mathrm{16}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$$${find}\:\int_{\mathrm{0}.\mathrm{5}} ^{\mathrm{3}.\mathrm{5}} {f}\left({x}\right)\:{dx}\:{using}\:{trapezoidal}\:{method} \\ $$$${then}\:{find}\:{the}\:{max}\:{and}\:{min}\:{value}\:{of}\:{the}\:{error} \\ $$$$\:{with}\:{the}\:{given}\:{n}\:{steps} \\ $$$${x}_{{n}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}_{{n}} \right) \\…

1-e-2x-e-2x-dx-

Question Number 61966 by aliesam last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −{e}^{−\mathrm{2}{x}} }\:{dx} \\ $$ Commented by kaivan.ahmadi last updated on 12/Jun/19 $$\int\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} −\frac{\mathrm{1}}{{e}^{\mathrm{2}{x}} }}{dx}=\int\frac{{e}^{\mathrm{2}{x}} }{{e}^{\mathrm{2}{x}}…