Category: Integration

Question Number 39381 by rahul 19 last updated on 05/Jul/18 Answered by ajfour last updated on 06/Jul/18 $$f{}^{\prime }\left(x\right)⩾{\left[f\left(x\right)\right]}^3+{\left[f\left(x\right)\right]}^{-1}$$$$andf\left(0\right)=1,f\left(a\right)=3^{1/4}$$$$\Rightarrow\:\:\:\int_{\mathrm{1}} ^{\:\:{y}} \frac{{dy}}{{y}^{\mathrm{3}}…

Question Number 39379 by rahul 19 last updated on 05/Jul/18 Commented by MJS last updated on 06/Jul/18 $$\left(1\right)\mid \mid x\mid -\mid y\mid \mid =1$$$$\left(2\right)2a\mid x\mid \mid y\mid +1=2\mid x\mid +a\mid y\mid$$$$\left(\mathrm{1}\right)\:\:\:\:\:\begin{cases}{\left.{y}_{\mathrm{1}} \left.=−\mid{x}\mid−\mathrm{1};\:\mathrm{range}\left({y}_{\mathrm{1}} \right)=\right]−\infty;\:−\mathrm{1}\right]}\{{y}_{\mathrm{2}} =\mid{x}\mid+\mathrm{1};\:\mathrm{range}\left({y}_{\mathrm{2}}…

Question Number 39373 by maxmathsup by imad last updated on 05/Jul/18 $$findthevaluesofintegrals$$$$A={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}cos(x^2+x+1)dxandB={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}sin(x^2+x+1)dx$$ Commented by math…

Question Number 39375 by rahul 19 last updated on 05/Jul/18 Commented by rahul 19 last updated on 06/Jul/18 $$??????$$ Terms of Service Privacy…

Question Number 39369 by maxmathsup by imad last updated on 05/Jul/18 $$1)calculateF\left(x\right)={\int }_1^{\sqrt{x}}\frac{arctan\left(t\right)}{t^2}dtwithx⩾1$$$$2)calculate{A}_n={\int }_1^{\sqrt{n}}\frac{arctan\left(t\right)}{t^2}dtandfind{lim}_{n\to +\mathrm{\infty }}{A}_n$$ Commented…