Category: Integration

Question Number 127774 by Bird last updated on 02/Jan/21 $$calculate{u}_n={\int }_0^1{x}^n\sqrt{1-x^4}dx$$ Answered by Dwaipayan Shikari last updated on 02/Jan/21…

Question Number 127772 by Bird last updated on 02/Jan/21 $$calculate{\int }_0^{2\pi }\frac{dx}{{(cosx+2sinx)}^2}$$ Answered by mathmax by abdo last updated on 02/Jan/21 $$\mathrm{I}\:=\int_{\mathrm{0}}…

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…