A) 1
B) 3
C) 2
D) 4
Correct Answer: C
Solution :
Given,\[\int_{1}^{b}{(b-4x)}dx\ge 6-5b\]and\[b>1\] \[\Rightarrow \] \[\left[ bx-\frac{4{{x}^{2}}}{2} \right]_{1}^{b}\ge 6-5b\] \[\Rightarrow \] \[{{b}^{2}}-2{{b}^{2}}-b+2\ge 6-5b\] \[\Rightarrow \] \[-{{b}^{2}}-b+2\ge 6\] \[\Rightarrow \] \[-{{b}^{2}}+4b+2-6\ge 0\] \[\Rightarrow \] \[{{b}^{2}}-4b+4\le 0\] \[\Rightarrow \] \[{{(b-2)}^{2}}\le 0\] \[\therefore \] \[b-2=0\] \[\Rightarrow \] \[b=2\]
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