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Category: Integration

Question-79634

Question Number 79634 by TawaTawa last updated on 26/Jan/20 Commented by mathmax by abdo last updated on 27/Jan/20 Ω=π53π10xsin(2x)dxchangementx=π2tgivet=π2x$$\Omega=\int_{\frac{\mathrm{3}\pi}{\mathrm{10}}} ^{\frac{\pi}{\mathrm{5}}} \:\frac{\frac{\pi}{\mathrm{2}}−{t}}{{sin}\left(\mathrm{2}{t}\right)}\left(−{dt}\right)\:=\frac{\pi}{\mathrm{2}}\int_{\frac{\pi}{\mathrm{5}}}…

1-expicite-f-x-0-1-ln-1-xt-2-1-t-2-dt-with-x-0-2-calculate-0-1-ln-1-t-2-1-t-2-dt-and-0-1-ln-1-2t-2-1-t-2-dt-

Question Number 79627 by mathmax by abdo last updated on 26/Jan/20 1)expicitef(x)=01ln(1+xt2)1+t2dtwithx0$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}}…