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Category: Integration

1-find-f-a-0-2pi-dt-a-cos-2-t-sin-2-t-with-a-0-2-find-g-a-0-2pi-cos-2-t-a-cos-2-t-sin-2-t-2-dt-

Question Number 35225 by abdo mathsup 649 cc last updated on 16/May/18 $$\left.\mathrm{1}\right)\:{find}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\:\frac{{dt}}{{a}\:{cos}^{\mathrm{2}} {t}\:+\:{sin}^{\mathrm{2}} {t}}\:{with}\:{a}\neq\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{cos}^{\mathrm{2}} {t}}{\left({a}\:{cos}^{\mathrm{2}} {t}\:+{sin}^{\mathrm{2}} {t}\right)^{\mathrm{2}} }{dt}\:…

1-calculate-f-a-0-pi-dx-a-sin-2-x-cos-2-x-with-a-gt-0-2-find-the-value-of-g-a-0-pi-sin-2-x-a-sin-2-x-cos-2-x-2-dx-

Question Number 35226 by abdo mathsup 649 cc last updated on 16/May/18 $$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\:\frac{{dx}}{{a}\:{sin}^{\mathrm{2}} {x}\:\:+{cos}^{\mathrm{2}} {x}} \\ $$$${with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{sin}^{\mathrm{2}} {x}}{\left({a}\:{sin}^{\mathrm{2}} {x}\:+{cos}^{\mathrm{2}}…