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Category: Integration

Question-191567

Question Number 191567 by leandrosriv02 last updated on 26/Apr/23 Answered by Frix last updated on 26/Apr/23 $$\int\frac{\sqrt{{x}}−\mathrm{1}}{{x}^{\pi} }{dx}=\int{x}^{\frac{\mathrm{1}}{\mathrm{2}}−\pi} {dx}−\int{x}^{−\pi} {dx} \\ $$$$\mathrm{Which}\:\mathrm{is}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{using}\:\int{x}^{{r}} {dx}=\frac{{x}^{{r}+\mathrm{1}} }{{r}+\mathrm{1}} \\…

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

Question Number 126000 by bramlexs22 last updated on 16/Dec/20 $$\:\:\:\int\:\frac{{dx}}{\left({x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}}}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 16/Dec/20 $$\int\frac{\mathrm{1}}{\left({x}−\mathrm{1}\right)\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1}}}{dx}\:=\:{sec}^{−\mathrm{1}} \left({x}−\mathrm{1}\right)+{C} \\…

Find-the-Riemann-sum-for-the-given-function-with-the-specified-number-of-intervals-using-left-endpoints-f-x-4ln-x-2x-1-x-4-n-7-Round-your-answer-to-two-decimal-places-

Question Number 125997 by bramlexs22 last updated on 16/Dec/20 $${Find}\:{the}\:{Riemann}\:{sum}\:{for}\:{the} \\ $$$${given}\:{function}\:{with}\:{the}\:{specified} \\ $$$${number}\:{of}\:{intervals}\:{using}\:{left} \\ $$$${endpoints}\:{f}\left({x}\right)=\:\mathrm{4ln}\:{x}+\mathrm{2}{x}\:;\:\mathrm{1}\leqslant{x}\leqslant\mathrm{4} \\ $$$${n}=\mathrm{7}\:.\:{Round}\:{your}\:{answer}\:{to}\:{two} \\ $$$${decimal}\:{places}\:? \\ $$ Answered by liberty…

Question-125986

Question Number 125986 by Ñï= last updated on 16/Dec/20 Answered by Dwaipayan Shikari last updated on 16/Dec/20 $$−\mathrm{2}{tan}^{−\mathrm{1}} \left(\frac{{cos}\left(\frac{{t}}{\mathrm{2}}−\frac{{sint}}{\mathrm{2}}\right)}{{sin}\left(\frac{{t}}{\mathrm{2}}+\frac{{sint}}{\mathrm{2}}\right)}\right)+{C} \\ $$ Commented by Dwaipayan Shikari…

0-pi-2-dx-1-sin-x-

Question Number 191519 by Acem last updated on 25/Apr/23 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{\mathrm{1}+\:\mathrm{sin}\:{x}} \\ $$ Answered by BaliramKumar last updated on 25/Apr/23 $$\frac{\mathrm{1}\left(\mathrm{1}−\mathrm{sinx}\right)}{\left(\mathrm{1}+\mathrm{sinx}\right)\left(\mathrm{1}−\mathrm{sinx}\right)}\:=\:\frac{\mathrm{1}−\mathrm{sinx}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} \\ $$$$\int_{\mathrm{0}}…

cot-x-ln-sin-x-dx-

Question Number 125965 by bramlexs22 last updated on 16/Dec/20 $$\:\:\:\:\int\:\mathrm{cot}\:{x}\:\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)\:{dx}\:? \\ $$ Answered by Lordose last updated on 16/Dec/20 $$ \\ $$$$\int\mathrm{cot}\left(\mathrm{x}\right)\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{x}\right)\right)\mathrm{dx}\:\overset{\mathrm{u}=\mathrm{ln}\left(\mathrm{sin}\left(\mathrm{x}\right)\right)} {=}\int\mathrm{udu}\:\:\: \\ $$$$=\:\frac{\mathrm{u}^{\mathrm{2}}…