Category: Integration

Question Number 139432 by normabaru last updated on 27/Apr/21 Answered by Jme Eduardo last updated on 27/Apr/21 $$\left(a\right)ifx=t^{2}andy=t$$$$$$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{2}{t}^{\mathrm{4}} }{{t}^{\mathrm{4}}…

Question Number 139427 by Fikret last updated on 26/Apr/21 $$\underset{\sqrt{2}}{\stackrel{3\sqrt{2}}{\int }}\sqrt{x^2-2}dx+\underset{0}{\stackrel{4}{\int }}\sqrt{x^2+2}dx=?$$ Answered by MJS_new last updated on 27/Apr/21…

Question Number 8296 by tawakalitu last updated on 06/Oct/16 $$\mathrm{Give}\mathrm{the}\mathrm{integral}\mathrm{representation}\mathrm{of}2333!$$ Commented by 123456 last updated on 07/Oct/16 $${n}!=\underset{\mathrm{0}} {\overset{+\infty} {\int}}{t}^{{n}} {e}^{−{t}} {dt} \…

Question Number 8281 by tawakalitu last updated on 06/Oct/16 $$\int \frac{6\mathrm{sinx}\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}$$ Answered by Yozzias last updated on 06/Oct/16 $$\frac{\mathrm{sinx}}{\mathrm{sinx}+\mathrm{cosx}}=1-\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}}$$$$\therefore \mathrm{I}=\int \frac{\mathrm{sinxcosx}}{\mathrm{sinx}+\mathrm{cosx}}\mathrm{dx}=\int (1-\frac{\mathrm{cosx}}{\mathrm{sinx}+\mathrm{cosx}})\mathrm{cosxdx}$$$$=\int\left(\mathrm{cosx}−\frac{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}{\mathrm{sinx}+\mathrm{cosx}}\right)\mathrm{dx}…

Question Number 73751 by ~blr237~ last updated on 15/Nov/19 $$Findoutthevalueof$$$$J={\int }_0^{\mathrm{\infty }}{\int }_0^1(2e^{-2xy}-e^{-xy})dxdy$$ Commented by mathmax by abdo…