Question Number 17220 by Arnab Maiti last updated on 02/Jul/17 $$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{a}} ^{\:\mathrm{b}} {f}\left(\mathrm{kx}\right)\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{k}}\int_{\mathrm{ka}} ^{\:\mathrm{kb}} {f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by ajfour last updated on 02/Jul/17 $$\mathrm{let}\:\mathrm{kx}=\mathrm{t}\:\:\:\Rightarrow\:\:\:\mathrm{dx}=\frac{\mathrm{dt}}{\mathrm{k}}…
Question Number 17219 by Arnab Maiti last updated on 02/Jul/17 $$\int_{\mathrm{0}} ^{\:\mathrm{2a}} \mathrm{xy}\:\mathrm{dx}=?\:\:\mathrm{where}\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{0} \\ $$ Commented by Arnab Maiti last updated on…
Question Number 82755 by mathmax by abdo last updated on 23/Feb/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$ Commented by Ajao yinka last updated on…
Question Number 17210 by Arnab Maiti last updated on 02/Jul/17 $$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\Pi} {f}\left(\mathrm{sin}\:\mathrm{x}\right)\mathrm{dx}=\mathrm{2}×\int_{\mathrm{0}} ^{\:\frac{\Pi}{\mathrm{2}}} {f}\left(\mathrm{sin}\:\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by mrW1 last updated on 02/Jul/17 $$\mathrm{let}\:\mathrm{I}=\int_{\frac{\pi}{\mathrm{2}}}…
Question Number 17206 by Arnab Maiti last updated on 02/Jul/17 $$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{vallu}\:\mathrm{of}\:\int_{−\mathrm{a}} ^{\:\mathrm{a}} \mathrm{x}^{\mathrm{2}} \mathrm{y}\:\mathrm{dx}\:\:? \\ $$$$\mathrm{Where}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{0} \\ $$ Answered by mrW1 last…
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 $$\frac{\mathrm{r}}{\mathrm{n}}\rightarrow\mathrm{x}\:,\:\Rightarrow\:\mathrm{dx}\rightarrow\frac{\mathrm{1}}{\mathrm{n}} \\…
Question Number 17203 by Arnab Maiti last updated on 02/Jul/17 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}−\mathrm{x}+\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$ Commented by prakash jain last updated on 02/Jul/17…
Question Number 17204 by Arnab Maiti last updated on 02/Jul/17 $$\int_{\mathrm{0}} ^{\:\frac{\Pi}{\mathrm{2}}} \mathrm{sin}\theta\:\mathrm{cos}\theta\left(\mathrm{a}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta+\mathrm{b}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \theta\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \mathrm{d}\theta \\ $$ Answered by prakash jain last…
Question Number 17180 by shankarnstephen last updated on 02/Jul/17 Commented by prakash jain last updated on 02/Jul/17 $$\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} \\ $$ Terms…
Question Number 82700 by jagoll last updated on 23/Feb/20 $$\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}}…