Category: Integration

Question Number 40141 by maxmathsup by imad last updated on 16/Jul/18 $$find{\int }_0^{\frac{\pi }{2}}\frac{dx}{3+sinx}$$ Commented by maxmathsup by imad last updated on 19/Jul/18…

Question Number 40138 by maxmathsup by imad last updated on 16/Jul/18 $$let{a}_k={\int }_{-\frac{\pi }{2}+k\pi }^{-\frac{\pi }{2}+(k+1)\pi }{e}^{-t}costdt$$$$1)calculate{a}_k$$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\mid{a}_{{k}} \mid. \…

Question Number 40136 by maxmathsup by imad last updated on 16/Jul/18 $$let{A}_n={\int }_0^1{x}^n{e}^{-x}dx$$$$1)calculate{A}_{1}and{A}_2$$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\:{A}_{{n}+\mathrm{1}} =\left({n}+\mathrm{1}\right){A}_{{n}} \:−\frac{\mathrm{1}}{{e}} \…

Question Number 40132 by maxmathsup by imad last updated on 16/Jul/18 $$calculate{\int }_0^1\frac{dt}{{(1+t^2)}^3}$$ Commented by maxmathsup by imad last updated…

Question Number 40130 by maxmathsup by imad last updated on 16/Jul/18 $$calculate{\int }_0^{\frac{\pi }{4}}{cos}^{4}x{sin}^{2}xdx$$ Commented by math khazana by abdo last…