Category: Integration

Question Number 53119 by rahul 19 last updated on 18/Jan/19 $$Evaluate:$$$$1)\int \sqrt{\frac{2-x}{4+x}}dx$$$$2)\int \sqrt{\frac{x-2}{x-4}}dx$$$$3)\int \sqrt{(x-2)(x-4)}dx$$$$4)\int \frac{dx}{2\sin \mathit{x}+3\sec \mathit{x}}.$$ Commented by maxmathsup by…

Question Number 53114 by maxmathsup by imad last updated on 17/Jan/19 $$let{A}_n={\int }_0^{\mathrm{\infty }}\frac{xsin\left(nx\right)}{{(x^2+n^2)}^2}dxwithnintegrnaturalnot0$$$$1)findthevalueof{A}_n$$$$2)studytheconvergenceof\mathrm{\Sigma }{A}_n$$ Commented…

Question Number 53112 by maxmathsup by imad last updated on 21/Jan/19 $$calculate{\int }_0^{\pi }\frac{1+2sinx}{3+2cosx}dx$$$$letA={\int }_0^{\pi }\frac{1+2sinx}{3+2cosx}dxchangementtan\left(\frac{x}{2}\right)=tgive$$$${A}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{1}+\frac{\mathrm{4}{t}}{\mathrm{1}+{t}^{\mathrm{2}} }}{\mathrm{3}+\mathrm{2}\frac{\mathrm{1}−{t}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }}\:\frac{\mathrm{2}{dt}}{\mathrm{1}+{t}^{\mathrm{2}}…

Question Number 53080 by Abdo msup. last updated on 17/Jan/19 $$calculate{\int }_0^{\pi }\frac{{cos}^{2}x}{2+3sin\left(2x\right)}dx$$ Commented by maxmathsup by imad last updated on 17/Jan/19…

Question Number 53078 by gunawan last updated on 16/Jan/19 $${\int }_0^1\frac{1}{{(x^3+1)}^{3/2}}dx=\dots$$ Commented by MJS last updated on 17/Jan/19 $$\approx.\mathrm{774606} \…