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Category: Integration

lim-n-r-1-n-1-1-n-n-r-n-r-

Question Number 17205 by Arnab Maiti last updated on 02/Jul/17 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\frac{\mathrm{1}}{\mathrm{n}}\sqrt{\frac{\mathrm{n}+\mathrm{r}}{\mathrm{n}−\mathrm{r}}} \\ $$ Answered by ajfour last updated on 02/Jul/17 $$\frac{\mathrm{r}}{\mathrm{n}}\rightarrow\mathrm{x}\:,\:\Rightarrow\:\mathrm{dx}\rightarrow\frac{\mathrm{1}}{\mathrm{n}} \\…

Question-17180

Question Number 17180 by shankarnstephen last updated on 02/Jul/17 Commented by prakash jain last updated on 02/Jul/17 $$\int\frac{\mathrm{sin}\:{x}\centerdot{e}^{\mathrm{cos}\:{x}} −\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right){e}^{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}} }{{e}^{\mathrm{2sin}\:{x}} −\mathrm{2}{e}^{\mathrm{sin}\:{x}} +\mathrm{1}}{dx} \\ $$ Terms…

2dx-3x-5x-2-6-

Question Number 82700 by jagoll last updated on 23/Feb/20 $$\int\:\frac{\mathrm{2}{dx}}{\mathrm{3}{x}\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}}}\:? \\ $$ Commented by john santu last updated on 23/Feb/20 $$\int\:\frac{{d}\left({x}^{\mathrm{2}} \right)}{\mathrm{3}{x}^{\mathrm{2}} \:\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}}}\:,\:{let}\:{x}^{\mathrm{2}}…

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

Question Number 17086 by Joel577 last updated on 30/Jun/17 $$\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by Joel577 last updated on 30/Jun/17 $$\mathrm{How}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{like}\:\mathrm{this}? \\ $$$$\mathrm{Because}\:\mathrm{when}\:\mathrm{I}\:\mathrm{graph}\:\mathrm{the}\:\mathrm{function},…

sin-101x-sinx-99-dx-

Question Number 82617 by necxxx last updated on 23/Feb/20 $$\int\mathrm{sin}\:\left(\mathrm{101}{x}\right)\left({sinx}\right)^{\mathrm{99}} {dx} \\ $$ Answered by TANMAY PANACEA last updated on 23/Feb/20 $$\int{sin}\left({n}+\mathrm{1}\right){xsin}^{{n}−\mathrm{1}} {xdx}\:\:\:\:{n}=\mathrm{100} \\ $$$$\int\left({sinnxcosx}+{cosnxsinx}\right){sin}^{{n}−\mathrm{1}}…