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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

$\int \limits_1^6 (6-4x) dx \leq 6-5b \;\&\;6 > 1$ Find 'b' value

\[\begin {array} {1 1} (a)\;1 \\ (b)\;3 \\ (c)\;2 \\ (d)\;4 \end {array}\]

1 Answer

$\int \limits _1^6 (b-4x\;dx)\;dx \geq 6-5b\qquad ;\qquad 6 < 1 $
$[bx-2x^2]_1^6 \geq 6-5b$
$[b^2-2b^2-b+2] \geq 6-5b$
$-[b^2 +b -2] \geq 6- 5b$
$b^2 +4 b -4 >0$
$(b-2)^2 \leq 0$
$| b-2| \leq 0$
$b=2$
Hence c is the correct answer.
answered Dec 17, 2013 by meena.p
 

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