Category: Integration

Question Number 218322 by shunmisaki007 last updated on 06/Apr/25 $$\mathrm{Evaluate}\underset{0}{\stackrel{\frac{\pi }{2}}{\int }}\frac{\sin \left(x\right)}{{\sin }^3\left(x\right)+{\cos }^3\left(x\right)}dx.$$ Answered by Ghisom last updated on 06/Apr/25 $$\underset{\mathrm{0}} {\overset{\pi/\mathrm{3}}…

Question Number 218148 by mnjuly1970 last updated on 30/Mar/25 $$$$$$\mathrm{I}={\int }_0^{\mathrm{\infty }}\frac{\sin \left(\sqrt{x}\right)}{\sqrt[4]{e^x}}dx=?$$$$$$ Answered by MrGaster last updated on…

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 $$$$$$provethat:$$$$$$$$$$$$\mathrm{I}={\int }_0^{\mathrm{\infty }}\frac{sin\left(\pi x\right)sin\left(2\pi x\right)sin\left(3\pi x\right)}{x^3}={\pi }^3$$$$ \…