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Category: Integration

pi-4-pi-cos2x-dx-

Question Number 8806 by tawakalitu last updated on 28/Oct/16 $$\int_{\frac{\pi}{\mathrm{4}}} ^{\pi} \mathrm{cos2x}\:\mathrm{dx} \\ $$ Commented by ridwan balatif last updated on 29/Oct/16 $$\int_{\frac{\pi}{\mathrm{4}}} ^{\pi} \mathrm{cos2x}\:\mathrm{dx}=\:\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{sin2x}\right)\underset{\frac{\pi}{\mathrm{4}}}…

f-x-4-3-2-1-3-

Question Number 8794 by faster1998 last updated on 28/Oct/16 $${f}\left({x}\right)=×^{\frac{\mathrm{4}}{\mathrm{3}}} −\mathrm{2}×^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Commented by ridwan balatif last updated on 28/Oct/16 $$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} .\mathrm{x}−\mathrm{2x}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}}…

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

Question Number 8762 by tawakalitu last updated on 26/Oct/16 $$\int\mathrm{x}^{\mathrm{2}} \left(\mathrm{2x}\:+\:\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}} \:\mathrm{dx} \\ $$ Answered by sou1618 last updated on 26/Oct/16 $${I}=\int{x}^{\mathrm{2}} \sqrt{\mathrm{2}{x}+\mathrm{1}}{dx} \\ $$$${t}=\mathrm{2}{x}+\mathrm{1}…

x-3x-1-dx-

Question Number 8763 by tawakalitu last updated on 26/Oct/16 $$\int\mathrm{x}\sqrt{\mathrm{3x}\:+\:\mathrm{1}}\:\:\mathrm{dx} \\ $$ Commented by FilupSmith last updated on 26/Oct/16 $${u}=\mathrm{3}{x}+\mathrm{2}\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{3}}\left({u}−\mathrm{2}\right) \\ $$$${du}=\mathrm{3}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\int\mathrm{3}{x}\sqrt{\mathrm{3}{x}+\mathrm{2}}{dx} \\…