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Category: Integration

Question-205315

Question Number 205315 by cherokeesay last updated on 15/Mar/24 Answered by MM42 last updated on 16/Mar/24 $$\left[{x}\right]+\left[{x}−\frac{\mathrm{1}}{\mathrm{2}}\right]=\left[\mathrm{2}{x}\right]−\mathrm{1} \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{\left[{x}\right]} \left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right){dx}=\left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right){x}\mid_{\mathrm{0}} ^{\left[{x}\right]} \\ $$$$=\left(\left[\mathrm{2}{x}\right]−\mathrm{1}\right)\left[{x}\right] \\…

pi-2-pi-2-8-2-cosx-1-e-sinx-1-sin-4-x-dx-api-blog-3-2-2-then-find-a-b-

Question Number 205279 by gopikrishnan last updated on 14/Mar/24 $$\underset{-\pi/\mathrm{2}} {\int}^{\pi/\mathrm{2}} \frac{\mathrm{8}\sqrt{\mathrm{2}}{cosx}}{\left(\mathrm{1}+\overset{{sinx}} {{e}}\right)\left(\mathrm{1}+{si}\overset{\mathrm{4}} {{n}x}\right)}{dx}={a}\pi+{blog}\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)\:{then}\:{find}\:{a}+{b} \\ $$ Answered by Berbere last updated on 14/Mar/24 $${x}\rightarrow−{x} \\…

Question-205269

Question Number 205269 by cherokeesay last updated on 14/Mar/24 Answered by som(math1967) last updated on 14/Mar/24 $$\:\int_{−\mathrm{2}} ^{\mathrm{2}} \mathrm{2}{f}\left({x}\right){dx}\:\:\left[\:\because{f}\left({x}\right)={f}\left(−{x}\right)\right] \\ $$$$=\mathrm{2}\int_{−\mathrm{2}} ^{\mathrm{2}} {f}\left({x}\right){dx} \\ $$$$=\mathrm{4}\int_{\mathrm{0}}…

pls-how-to-calculate-this-1-2-1-ln-x-1-x-dx-

Question Number 205264 by pticantor last updated on 13/Mar/24 $$\boldsymbol{{pls}}\:\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{calculate}}\:\boldsymbol{{this}}? \\ $$$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \frac{\boldsymbol{{ln}}\left(\boldsymbol{{x}}+\mathrm{1}\right)}{\boldsymbol{{x}}}\boldsymbol{{dx}} \\ $$ Answered by Berbere last updated on 13/Mar/24 $$=−\left(−\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}}…

0-pi-x-2-cos-2-x-xsin-x-cos-x-1-1-xsin-x-2-dx-

Question Number 205248 by universe last updated on 13/Mar/24 $$\:\:\:\int_{\mathrm{0}} ^{\pi} \:\frac{{x}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \left({x}\right)−{x}\mathrm{sin}\left({x}\right)−\mathrm{cos}\left({x}\right)−\mathrm{1}}{\left(\mathrm{1}+{x}\mathrm{sin}\left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$ Answered by Berbere last updated on 13/Mar/24 $$\left(\frac{{f}\left({x}\right)}{\mathrm{1}+{xsin}\left({x}\right)}+{g}\left({x}\right)\right)^{'}…