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Category: Integration

the-function-f-with-variable-x-satisfies-the-equation-x-2-f-x-2x-f-x-arctan-x-for-0-lt-arctan-x-lt-pi-2-and-f-1-pi-4-find-f-x-

Question Number 140896 by bramlexs22 last updated on 14/May/21 $$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\:\mathrm{with}\:\mathrm{variable}\:\mathrm{x} \\ $$$$\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{x}^{\mathrm{2}} \:\mathrm{f}\:'\left(\mathrm{x}\right)\:+\mathrm{2x}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{arctan}\:\mathrm{x}\:\mathrm{for}\: \\ $$$$\mathrm{0}\:<\:\mathrm{arctan}\:\mathrm{x}\:<\frac{\pi}{\mathrm{2}}\:\mathrm{and}\:\mathrm{f}\left(\mathrm{1}\right)=\frac{\pi}{\mathrm{4}}. \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$ Answered by EDWIN88 last…

Question-9822

Question Number 9822 by ridwan balatif last updated on 06/Jan/17 Answered by sandy_suhendra last updated on 06/Jan/17 $$\mathrm{f}\:'\left(\mathrm{x}\right)=\mathrm{k}\left(\mathrm{3x}^{\mathrm{2}} −\mathrm{12x}+\mathrm{9}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{3}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{0} \\…

Question-9821

Question Number 9821 by ridwan balatif last updated on 06/Jan/17 Commented by prakash jain last updated on 08/Jan/17 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right) \\ $$$$\mathrm{and}\:\int_{\mathrm{0}} ^{\mathrm{2}} {f}\left({x}\right){dx}={B}…

Advanced-Calculus-find-the-value-of-the-infinite-series-n-1-1-n-1-H-2n-2n-1-

Question Number 140885 by mnjuly1970 last updated on 13/May/21 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…….\:{Advanced}\:::::::::::\bigstar\bigstar\bigstar::::::::::\:{Calculus}……. \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:{the}\:{infinite}\:{series}:: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\Theta\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \mathrm{H}_{\:\mathrm{2}{n}} }{\mathrm{2}{n}−\mathrm{1}}\:=\:??? \\ $$$$\:\:\:\:\:\:\:\:\:\:…….\mathscr{M}.\mathscr{N}.{july}.\mathrm{1970}…….. \\…

0-1-ln-2-ln-1-x-2-1-x-dx-

Question Number 140866 by liberty last updated on 13/May/21 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{ln}\:\mathrm{2}−\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{1}−\mathrm{x}}\:\mathrm{dx}\:=?\: \\ $$ Answered by mindispower last updated on 15/May/21 $$=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\int_{\mathrm{0}} ^{{x}}…

Determine-whether-the-improper-integral-converges-or-diverges-1-2x-7-7x-3-5x-2-1-dx-

Question Number 140823 by liberty last updated on 13/May/21 $$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{improper} \\ $$$$\mathrm{integral}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges}\: \\ $$$$\int_{\mathrm{1}} ^{\:\infty} \:\frac{\mathrm{2x}+\mathrm{7}}{\mathrm{7x}^{\mathrm{3}} +\mathrm{5x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}\: \\ $$ Commented by liberty last updated…