Category: Integration

Question Number 8794 by faster1998 last updated on 28/Oct/16 $$f\left(x\right)={\times }^{\frac{4}{3}}-2{\times }^{\frac{1}{3}}$$ Commented by ridwan balatif last updated on 28/Oct/16 $$\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^{\frac{1}{3}}.\mathrm{x}-{2\mathrm{x}}^{\frac{1}{3}}$$$$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question Number 8782 by uchechukwu okorie favour last updated on 27/Oct/16 $$evaluate;\int \frac{{\sin }^{-1}x}{\sqrt{1-x^2}}dx$$ Answered by prakash jain last updated on 27/Oct/16 $$\mathrm{sin}^{−\mathrm{1}}…

Question Number 8762 by tawakalitu last updated on 26/Oct/16 $$\int {\mathrm{x}}^2{(2\mathrm{x}+1)}^{1/2}\mathrm{dx}$$ Answered by sou1618 last updated on 26/Oct/16 $$I=\int x^2\sqrt{2x+1}dx$$$${t}=\mathrm{2}{x}+\mathrm{1}…

Question Number 139826 by qaz last updated on 01/May/21 $$\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{\sin \left[(n-1)x\right]}{4^{n+1}}=?$$ Answered by mnjuly1970 last updated on 01/May/21 $$\:\:\:\:\:\Omega:=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{sin}\left(\left({n}−\mathrm{1}\right){x}\right)}{\mathrm{4}^{{n}+\mathrm{1}}…

Question Number 8734 by tawakalitu last updated on 24/Oct/16 $$\mathrm{Evaluate}\mathrm{the}\mathrm{integral}$$$$\int [\mathrm{a}(\stackrel{\bullet }{\mathrm{b}}.\mathrm{a}+\mathrm{b}.\stackrel{\bullet }{\mathrm{a}})+\stackrel{\bullet }{\mathrm{a}}(\mathrm{b}.\mathrm{a})-2(\stackrel{\bullet }{\mathrm{a}}.\mathrm{a})\mathrm{b}-\stackrel{\bullet }{\mathrm{b}}\mid \mathrm{a}{\mid }^2]\mathrm{dt}$$$$\mathrm{In}\mathrm{which}\stackrel{\bullet }{\mathrm{a}},\stackrel{\bullet }{\mathrm{b}}\mathrm{are}\mathrm{the}\mathrm{derivatives}\mathrm{of}\mathrm{a},\mathrm{b}\mathrm{with}$$$$\mathrm{respect}\:\mathrm{to}\:\mathrm{t} \…