Category: Integration

Question Number 61328 by maxmathsup by imad last updated on 01/Jun/19 $$letf\left(a\right)={\int }_0^1\frac{sin\left(2x\right)}{1+{ax}^2}dxwith\mid a\mid <1$$$$1)approximatef\left(a\right)byapolynom$$$$2)findthevalue\left(perhapsnotexact\right)of{\int }_0^1\frac{sin\left(2x\right)}{1+2x^2}dx$$$$\left.\mathrm{3}\right)\:{let}\:{g}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…

Question Number 192388 by sudipmoi last updated on 16/May/23 Answered by aleks041103 last updated on 22/May/23 $$p>0$$$$\int_{\mathrm{1}} ^{\:\infty} \frac{{sin}\left({x}\right){dx}}{{x}^{{p}} }=\left[−\frac{{cos}\left({x}\right)}{{x}^{{p}} }\right]_{\mathrm{1}} ^{\infty} −\int_{\mathrm{1}}…

Question Number 126788 by john_santu last updated on 24/Dec/20 $$\sigma =\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\sqrt{x}{e}^{-x/4}dx=?$$ Answered by Ar Brandon last updated on 24/Dec/20 $$\mathrm{x}=\mathrm{u}^{\mathrm{2}} \:\Rightarrow\:\mathrm{dx}=\mathrm{2udu}…

Question Number 61237 by aliesam last updated on 30/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 61232 by maxmathsup by imad last updated on 30/May/19 $$let{U}_n={\int }_1^{+\mathrm{\infty }}\frac{\left[nx\right]-\left[(n-1)x\right]}{x^3}dxwithn⩾1$$$$1)find{U}_{n}intermsofn$$$$2)find{lim}_{n\to +\mathrm{\infty }}{U}_n$$$$\left.\mathrm{3}\right)\:{study}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty}…