Category: Integration

Question Number 198948 by ArifinTanjung last updated on 26/Oct/23 $${\int }_1^3\frac{\mathrm{x}-2}{{\mathrm{x}}^2-4\mathrm{x}}\mathrm{dx}=\dots .$$ Answered by ajfour last updated on 26/Oct/23 $${I}=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\mathrm{1}} ^{\:\mathrm{1}} \frac{\mathrm{2}{tdt}}{{t}^{\mathrm{2}}…

Question Number 198802 by MathedUp last updated on 24/Oct/23 $$\mathrm{radius}r\mathrm{circle};x^2+y^2+z^2=r^2$$$$\hat{\mathbf{F}}(x,y,z)=yz{\hat{\mathbf{e}}}_1+x{\hat{\mathbf{e}}}_2-xy{\hat{\mathbf{e}}}_3$$$$\mathrm{Find}\:\mathrm{flux}\:\boldsymbol{\rho}=\int\int_{\:\boldsymbol{\Sigma}} \:\hat {\boldsymbol{\mathrm{F}}}\centerdot\hat…

Question Number 198695 by universe last updated on 23/Oct/23 $${\int }_0^{\mathrm{\infty }}\frac{{\mathrm{e}}^{\mathrm{at}}-{\mathrm{e}}^{-\mathrm{at}}}{{\mathrm{e}}^{\pi \mathrm{t}}-{\mathrm{e}}^{-\pi \mathrm{t}}}\mathrm{dt}=??$$ Answered by witcher3 last updated on 25/Oct/23…

Question Number 198496 by mnjuly1970 last updated on 21/Oct/23 $$$$$$Aniceseries$$$$If,\mathrm{\Omega }=\underset{n=2}{\sum ^{\mathrm{\infty }}}\frac{1}{n^2+n-1}=\frac{\pi tan\left(a\pi \right)}{b}$$$$\Rightarrow findthevalueof\frac{b}{a}=?$$$$$$ Commented by…

Question Number 198420 by Mingma last updated on 19/Oct/23 Answered by Frix last updated on 19/Oct/23 $$\int\frac{{x}^{\mathrm{2}} }{\left(\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} }{dx}\:\underset{{dx}=−\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }}{\mathrm{4}{t}}} {\overset{{t}=\frac{\mathrm{2}+\sqrt{\mathrm{3}+\mathrm{4}{x}−\mathrm{4}{x}^{\mathrm{2}} }}{\mathrm{2}{x}−\mathrm{1}}} {=}}\: \…