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Category: Integration

Question-175305

Question Number 175305 by cortano1 last updated on 26/Aug/22 Answered by mr W last updated on 27/Aug/22 $${let}\:{t}=\frac{{x}}{\mathrm{6}} \\ $$$$\mathrm{6}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{36}}} \frac{\mathrm{1}−\mathrm{cos}\:\mathrm{2}{t}}{\mathrm{sin}\:\mathrm{3}{t}}{dt} \\ $$$$=\mathrm{12}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{36}}}…

find-f-a-0-dx-x-3-a-3-with-a-gt-0-2-find-g-a-0-dx-x-3-a-3-2-3-find-the-value-of-0-dx-1-x-3-2-4-find-the-value-of-0-dx-8x-3-1-

Question Number 44202 by abdo.msup.com last updated on 23/Sep/18 $${find}\:\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{3}} \:+{a}^{\mathrm{3}} }\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){find}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{3}} \:+{a}^{\mathrm{3}} \right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}}…

let-f-x-0-1-ln-1-xt-2-t-2-dt-with-x-R-1-find-a-explicit-form-of-f-x-2-calculate-0-1-ln-1-t-2-t-2-dt-3-calculate-0-1-ln-1-2t-2-t-2-dt-4-calculate-0-1-ln-1-t-2

Question Number 44201 by abdo.msup.com last updated on 23/Sep/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:\:{with}\:{x}\:\in{R} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}}…

1-find-dx-x-2-x-1-x-2-x-1-2-calculate-0-1-dx-x-2-x-1-x-2-x-1-

Question Number 44179 by abdo.msup.com last updated on 22/Sep/18 $$\left.\mathrm{1}\right)\:{find}\:\int\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}} \\ $$$$\left.\mathrm{2}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\frac{{dx}}{\:\sqrt{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} −{x}\:+\mathrm{1}}} \\ $$ Commented by maxmathsup by imad…

find-f-x-0-pi-sin-2-t-x-2-2x-cost-1-2-dt-2-find-the-value-of-0-pi-sin-2-t-x-2-cost-1-2-dt-

Question Number 44178 by abdo.msup.com last updated on 22/Sep/18 $${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −\mathrm{2}{x}\:{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}^{\mathrm{2}} {t}}{\left({x}^{\mathrm{2}} −{cost}\:+\mathrm{1}\right)^{\mathrm{2}} }{dt} \\ $$ Terms…

find-f-a-1-dx-ch-2-x-a-sh-2-x-2-find-the-value-of-1-dx-ch-2-x-2sh-2-x-

Question Number 44175 by abdo.msup.com last updated on 22/Sep/18 $${find}\:\:{f}\left({a}\right)\:=\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dx}}{{ch}^{\mathrm{2}} {x}\:+{a}\:{sh}^{\mathrm{2}} {x}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{{dx}}{{ch}^{\mathrm{2}} {x}+\mathrm{2}{sh}^{\mathrm{2}} {x}} \\ $$ Commented by maxmathsup…