Category: Integration

Question Number 217881 by OmoloyeMichael last updated on 23/Mar/25 Answered by vnm last updated on 23/Mar/25 $${\int }_0^{\pi /2}x(\frac{\sin x}{1+{\cos }^{2}x}+\frac{\cos x}{1+{\sin }^{2}x})dx=I$$$${f}\left({x}\right)=\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} {x}}…

Question Number 217804 by mnjuly1970 last updated on 21/Mar/25 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 217761 by mnjuly1970 last updated on 20/Mar/25 $$$$$$provethat:$$$$$$$$$$$$\mathrm{I}={\int }_0^{\mathrm{\infty }}\frac{sin\left(\pi x\right)sin\left(2\pi x\right)sin\left(3\pi x\right)}{x^3}={\pi }^3$$$$ \…

Question Number 217683 by MrGaster last updated on 18/Mar/25 $$\mathrm{Prove}:{\int }_0^1\sqrt{\frac{\sqrt{K^2+36K^{\prime 2}}+6K^{{}^{\prime }}}{K^2+36K^{{}^{\prime }2}}}\frac{dk}{\sqrt{k}{(1-k^2)}^{\frac{2}{3}}}=\sqrt{\pi }(\sqrt{2}-\sqrt{\frac{4-2\sqrt{2}}{3}})$$ Terms of Service Privacy…

Question Number 217431 by peter frank last updated on 13/Mar/25 Answered by Frix last updated on 13/Mar/25 $$\mathrm{Simply}\mathrm{by}\mathrm{parts}:$$$$u^{\prime }=\frac{1}{{(x+1)}^2}\to u=-\frac{1}{x+1}$$$${v}={x}\mathrm{e}^{{x}} \:\rightarrow\:{v}'=\left({x}+\mathrm{1}\right)\mathrm{e}^{{x}} \…