Category: Integration

Question Number 23432 by gopikrishnan005@gmail.com last updated on 30/Oct/17 $${\int }_0^{a}f\left(x\right)dx=$$ Answered by Joel577 last updated on 31/Oct/17 $$\mathrm{Let}F\left(x\right)\mathrm{is}\mathrm{an}\mathrm{anti}\mathrm{derivative}\mathrm{of}f\left(x\right)$$$${I}\:=\:\underset{\mathrm{0}} {\overset{{a}}…

Question Number 88955 by M±th+et£s last updated on 14/Apr/20 $$hello$$$$floorfunction$$$${\int }_a^b\lfloor x\rfloor dxa,b\in zandb>a$$$$=\int_{\mathrm{0}} ^{{b}} \lfloor{x}\rfloor\:{dx}\:−\int_{\mathrm{0}} ^{{a}} \lfloor{x}\rfloor\:{dx}\:=\frac{{b}^{\mathrm{2}} −{b}}{\mathrm{2}}−\frac{{a}^{\mathrm{2}} −{a}}{\mathrm{2}}\:….\left(\mathrm{1}\right) \…

Question Number 23402 by RoachDN last updated on 29/Oct/17 Commented by Tinkutara last updated on 29/Oct/17 $$I=\underset{0}{\stackrel{1}{\int }}\frac{\sin xdx}{1+x^3}$$ Commented by RoachDN…

Question Number 88930 by mathmax by abdo last updated on 13/Apr/20 $$find{A}_{\lambda }={\int }_0^{\mathrm{\infty }}\frac{cos\left(\lambda x\right)}{{(x^2-x+1)}^2}dxwith\lambda >0$$$$2)findthevalueof{\int }_0^{\mathrm{\infty }}\frac{cos\left(3x\right)}{{(x^2-x+1)}^2}dx$$…

Question Number 88928 by mathmax by abdo last updated on 13/Apr/20 $$calculate{\int }_0^{\mathrm{\infty }}\frac{dx}{{(x^4+x^2+3)}^2}$$ Commented by mathmax by abdo last…