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Question-185708




Question Number 185708 by mokys last updated on 26/Jan/23
Answered by mr W last updated on 26/Jan/23
t=4 log_2  x=((4 ln x)/(ln 2))  dt=(4/(x ln 2))dx  ∫_1 ^8 ((f(4 log_2  x))/x)dx  =((ln 2)/4)∫_0 ^(12) f(t)dt  =((ln 2)/4)×20  =5 ln 2
$${t}=\mathrm{4}\:\mathrm{log}_{\mathrm{2}} \:{x}=\frac{\mathrm{4}\:\mathrm{ln}\:{x}}{\mathrm{ln}\:\mathrm{2}} \\ $$$${dt}=\frac{\mathrm{4}}{{x}\:\mathrm{ln}\:\mathrm{2}}{dx} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{8}} \frac{{f}\left(\mathrm{4}\:\mathrm{log}_{\mathrm{2}} \:{x}\right)}{{x}}{dx} \\ $$$$=\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}}\int_{\mathrm{0}} ^{\mathrm{12}} {f}\left({t}\right){dt} \\ $$$$=\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{4}}×\mathrm{20} \\ $$$$=\mathrm{5}\:\mathrm{ln}\:\mathrm{2} \\ $$
Commented by mokys last updated on 27/Jan/23
thank you sir
$${thank}\:{you}\:{sir} \\ $$$$ \\ $$
Answered by Rajpurohith last updated on 26/Jan/23
Commented by mokys last updated on 27/Jan/23
thank you sir
$${thank}\:{you}\:{sir} \\ $$

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