Category: Integration

Question Number 32958 by artibunja last updated on 07/Apr/18 Commented by MJS last updated on 07/Apr/18 $$\frac{x^2-3x-10}{3x^2-5x+2}=\frac{1}{3}+\frac{(-3+\frac{5}{3})x+(-10-\frac{2}{3})}{3x^2-5x+2}=$$$$=\frac{1}{3}-\frac{4}{3}\times \frac{x+8}{3x^2-5x+2}$$$$\mathrm{3}{x}^{\mathrm{2}}…

Question Number 32939 by abdo imad last updated on 06/Apr/18 $$1)studytheconvergenceof{\int }_0^1\frac{x^p}{1+x}dx$$$$2)find{lim}_{p\to \mathrm{\infty }}{\int }_0^1\frac{x^p}{1+x}dx.$$ Commented by abdo…

Question Number 98463 by pranesh last updated on 14/Jun/20 Answered by maths mind last updated on 15/Jun/20 $$\underset{k=1}{\sum ^{99}}\frac{x^k}{k}=\int \frac{1-x^{99}}{1-x}dx$$$$\left({cot}\left({x}\right)+……+\frac{{cot}^{\mathrm{99}} \left({x}\right)}{\mathrm{99}}\right)+\int\left(\mathrm{1}+{cot}\left({x}\right)\right)\left(\mathrm{1}+{cot}^{\mathrm{99}}…

Question Number 98445 by mathmax by abdo last updated on 14/Jun/20 $$\mathrm{give}\mathrm{at}\mathrm{form}\mathrm{of}\mathrm{serie}{\mathrm{U}}_{\mathrm{n}}={\int }_0^1\frac{{\mathrm{x}}^{\mathrm{n}}\ln \left(\mathrm{x}\right)}{{(1+\mathrm{x})}^2}\mathrm{dx}$$ Answered by mathmax by abdo last…

Question Number 98426 by mathmax by abdo last updated on 13/Jun/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)={\int }_{\frac{\pi }{4}}^{\frac{\pi }{3}}\frac{\mathrm{dt}}{\mathrm{x}+\mathrm{tant}}\mathrm{calculate}\mathrm{f}\left(\mathrm{x}\right)$$$$2)\mathrm{explicit}\mathrm{g}\left(\mathrm{x}\right)={\int }_{\frac{\pi }{4}}^{\frac{\pi }{3}}\frac{\mathrm{dt}}{{(\mathrm{x}+\mathrm{tant})}^2}$$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{integrals}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\mathrm{2}+\mathrm{tant}}\:\mathrm{and}\:\int_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:\frac{\mathrm{dt}}{\left(\mathrm{2}+\mathrm{tant}\right)^{\mathrm{2}}…