Category: Algebra

Question Number 159532 by HongKing last updated on 18/Nov/21 $$\mathrm{if}0<\mathrm{a}⩽\mathrm{b}\mathrm{then}:$$$$\underset{\mathbf{a}}{\stackrel{\mathbf{b}}{\int }}\frac{{\mathrm{x}}^{19}}{\sqrt{1+{\mathrm{x}}^{30}}}\mathrm{dx}⩾\log \sqrt[10]{\frac{2+{\mathrm{b}}^{20}}{2+{\mathrm{a}}^{20}}}$$$$$$ Terms of Service…

Question Number 159534 by HongKing last updated on 18/Nov/21 $$\mathrm{Find}:$$$$\mathbf{\Omega }=\underset{0}{\stackrel{1}{\int }}{\arctan }^2\left(\mathrm{x}\right)\mathrm{dx}$$$$$$ Answered by chhaythean last updated on…

Question Number 159528 by HongKing last updated on 18/Nov/21 $$\mathrm{Find}:$$$$\mathbf{\Omega }=\underset{0}{\stackrel{\frac{\mathit{\pi }}{6}}{\int }}\frac{\sin \left(\mathrm{x}\right)\cdot \sin (\mathrm{x}+\frac{\pi }{3})\cdot \sin (\mathrm{x}+\frac{2\pi }{3})}{\sin \left(3\mathrm{x}\right)+\cos \left(3\mathrm{x}\right)}\mathrm{dx}$$$$\mathrm{Answer}:\frac{\pi }{48}$$ Answered by mnjuly1970 last updated on 18/Nov/21…

Question Number 159517 by Khalmohmmad last updated on 18/Nov/21 $$\underset{x\to 0}{\lim }\frac{1}{x^2}(e^{-2x}-\frac{1+ax}{1+bx})$$$$a+b=?$$ Commented by tounghoungko last updated on 18/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{0}}…

Question Number 28434 by abdo imad last updated on 25/Jan/18 $$letgivethepolynomialp\left(x\right)={(x+1)}^n-{(x-1)}^{n}withn$$$$from{N}^{\ast }$$$$1)givethefactorisationofp\left(x\right)insideC\left[x\right]$$$$2)provethat\prod _{k=0}^{n-1}cotan\left(\frac{k\pi }{2p+1}\right)=\frac{1}{\sqrt{2p+1}}$$ Terms of…