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Question Number 50132 by CIRCLE001 last updated on 14/Dec/18

Let f  be a positive function. Let  I_1 =∫_(1−k) ^k x f{x(1−x} dx,   I_2 =∫_(1−k) ^k x f{x(1−x} dx,   where 2k−1>0. Then (I_1 /I_2 )  is

$$\mathrm{Let}\:{f}\:\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{function}.\:\mathrm{Let} \\ $$ $${I}_{\mathrm{1}} =\underset{\mathrm{1}−{k}} {\overset{{k}} {\int}}{x}\:{f}\left\{{x}\left(\mathrm{1}−{x}\right\}\:{dx},\:\right. \\ $$ $${I}_{\mathrm{2}} =\underset{\mathrm{1}−{k}} {\overset{{k}} {\int}}{x}\:{f}\left\{{x}\left(\mathrm{1}−{x}\right\}\:{dx},\:\right. \\ $$ $$\mathrm{where}\:\mathrm{2}{k}−\mathrm{1}>\mathrm{0}.\:\mathrm{Then}\:\frac{{I}_{\mathrm{1}} }{{I}_{\mathrm{2}} }\:\:\mathrm{is} \\ $$

Commented bytanmay.chaudhury50@gmail.com last updated on 14/Dec/18

in question I_1  and I_2  identical...pls check   question...

$${in}\:{question}\:{I}_{\mathrm{1}} \:{and}\:{I}_{\mathrm{2}} \:{identical}...{pls}\:{check}\: \\ $$ $${question}... \\ $$

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