Category: Integration

Question Number 62232 by aliesam last updated on 18/Jun/19 Commented by maxmathsup by imad last updated on 18/Jun/19 $$wehave\mid \alpha +\beta e^{i\theta }\mid =\mid \alpha +\beta cos\theta +i\beta sin\theta \mid =\sqrt{{(\alpha +\beta cos\theta )}^2+{\beta }^2{sin}^2\theta }\Rightarrow$$$${ln}\left(\mid\alpha+{ie}^{{i}\theta}…

Question Number 62220 by maxmathsup by imad last updated on 17/Jun/19 $$letf\left(x\right)={\int }_0^{\mathrm{\infty }}\frac{t^2}{x^6+t^6}dtwithx>0$$$$1)calculatef\left(x\right)$$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{t}^{\mathrm{2}} }{\left({x}^{\mathrm{6}} \:+{t}^{\mathrm{6}}…

Question Number 62208 by maxmathsup by imad last updated on 17/Jun/19 $$findf\left(a\right)=\int (x-a)\sqrt{x^2+a^2}dx$$ Commented by maxmathsup by imad last updated on 18/Jun/19…

Question Number 62207 by maxmathsup by imad last updated on 17/Jun/19 $$calculate\int \frac{x+3}{(x-2)\sqrt{x^2+x+1}}dx$$ Commented by maxmathsup by imad last updated on 18/Jun/19 $${I}\:=\int\:\frac{{x}−\mathrm{2}\:+\mathrm{5}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}}…

Question Number 62201 by maxmathsup by imad last updated on 17/Jun/19 $$calculate\int {\int }_W{e}^{x-2y}sin(x+2y)dxdy$$$$W=\{{(x,y)}^2/0⩽x⩽1and2⩽y⩽\sqrt{5}\}$$ Commented by mathmax by abdo last…