Category: Integration

Question Number 199213 by emilagazade last updated on 29/Oct/23 Answered by witcher3 last updated on 29/Oct/23 $${\int }_{\mathrm{a}}^{\mathrm{b}}(\mathrm{x}-\left[\mathrm{x}\right]-\frac{1}{2}){\mathrm{f}}^{\prime }\left(\mathrm{x}\right)=\mathrm{dx}$$$$=\underset{\mathrm{k}=\mathrm{a}} {\overset{\mathrm{b}−\mathrm{1}} {\sum}}\int_{\mathrm{k}} ^{\mathrm{k}+\mathrm{1}} \left(\mathrm{x}−\left[\mathrm{x}\right]−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{f}'\left(\mathrm{x}\right)\mathrm{dx}…

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…