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Category: Integration

calculate-x-3-2-x-dx-

Question Number 63720 by mathmax by abdo last updated on 08/Jul/19 $${calculate}\:\int\sqrt{\left({x}−\mathrm{3}\right)\left(\mathrm{2}−{x}\right)}{dx} \\ $$ Commented by Prithwish sen last updated on 08/Jul/19 $$\int\sqrt{−\mathrm{x}^{\mathrm{2}} +\mathrm{5x}\:−\mathrm{6}}\:\mathrm{dx}\:\:=\:\int\sqrt{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} −\left(\mathrm{x}−\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}}…

W-cos-5x-cos-4x-2cos-3x-1-dx-

Question Number 129223 by bramlexs22 last updated on 14/Jan/21 $$\:\mathrm{W}\:=\:\int\:\frac{\mathrm{cos}\:\mathrm{5x}+\mathrm{cos}\:\mathrm{4x}}{\mathrm{2cos}\:\mathrm{3x}−\mathrm{1}}\:\mathrm{dx}\: \\ $$ Answered by bobhans last updated on 14/Jan/21 $$\:{W}=\int\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)}{\mathrm{2cos}\:\mathrm{3}{x}−\mathrm{1}}\:{dx} \\ $$$$\:{W}=\int\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right).\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{2cos}\:\mathrm{3}{x}\mathrm{sin}\:\mathrm{3}{x}−\mathrm{sin}\:\mathrm{3}{x}}\:{dx} \\ $$$$\:{W}=\:\int\:\frac{\mathrm{2cos}\:\left(\frac{\mathrm{9}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{sin}\:\mathrm{6}{x}−\mathrm{sin}\:\mathrm{3}{x}}{dx} \\…

1-calculate-0-2pi-dt-cost-x-sint-wih-x-from-R-2-calculate-0-2pi-sint-cost-xsint-2-dt-3-find-the-value-of-0-2pi-dt-cos-2t-2sin-2t-

Question Number 63667 by mathmax by abdo last updated on 07/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dt}}{{cost}\:+{x}\:{sint}}\:\:\:{wih}\:{x}\:{from}\:{R}. \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sint}}{\left({cost}\:+{xsint}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\left[{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{dt}}{{cos}\left(\mathrm{2}{t}\right)+\mathrm{2}{sin}\left(\mathrm{2}{t}\right)}\right. \\ $$…