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Category: Integration

let-f-x-0-dt-t-2-2xt-1-1-find-a-explicit-form-of-f-x-2-cslvulste-0-dt-t-2-t-1-3-calculate-A-0-dt-t-2-2tan-t-1-4-calculate-g-x-0-tdt-

Question Number 44476 by abdo.msup.com last updated on 29/Sep/18 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{{t}^{\mathrm{2}} \:+\mathrm{2}{xt}−\mathrm{1}} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{cslvulste}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{{t}^{\mathrm{2}} \:+{t}−\mathrm{1}} \\ $$$$\left.\mathrm{3}\right){calculate}\:{A}\left(\theta\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dt}}{{t}^{\mathrm{2}} \:+\mathrm{2}{tan}\left(\theta\right){t}\:−\mathrm{1}}…

let-A-n-0-sin-n-t-e-t-dt-2-calculate-A-n-and-lim-n-n-A-n-3-study-the-convergence-of-n-A-n-

Question Number 44473 by abdo.msup.com last updated on 29/Sep/18 $${let}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{sin}\left({n}\left[{t}\right]\right){e}^{−{t}} {dt} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}} \:\:{and}\:{lim}_{{n}\rightarrow+\infty} {n}\:{A}_{{n}} \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{convergence}\:{of}\:\sum_{{n}} \:{A}_{{n}} \\ $$ Commented by…

dt-5cos-t-6sin-t-

Question Number 175531 by cortano1 last updated on 01/Sep/22 $$\:\int\:\frac{{dt}}{\mathrm{5cos}\:{t}+\mathrm{6sin}\:{t}}\:=? \\ $$ Answered by Ar Brandon last updated on 01/Sep/22 $${I}=\int\frac{{dt}}{\mathrm{5cos}{t}+\mathrm{6sin}{t}}\:,\:{x}=\mathrm{tan}\frac{{t}}{\mathrm{2}} \\ $$$$\:\:\:=\int\frac{\mathrm{2}}{\mathrm{5}\left(\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\right)+\mathrm{6}\left(\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}}…

let-f-x-0-x-sinx-a-2-x-4-dx-with-a-gt-0-1-find-a-explicit-form-of-f-a-2-find-g-a-0-xsinx-a-2-x-4-2-dx-3-find-the-value-of-0-x-sinx-x-4-1-d

Question Number 44466 by maxmathsup by imad last updated on 29/Sep/18 $${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{x}\:{sinx}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{4}} }{dx}\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{xsinx}}{\left({a}^{\mathrm{2}} \:+{x}^{\mathrm{4}} \right)^{\mathrm{2}} }{dx}…