A) 2a
B) \[2\sqrt{2}\]
C) \[\frac{a}{2}\]
D) none of these
Correct Answer: B
Solution :
We have, \[y=\left( 1+\frac{8}{{{x}^{2}}} \right)\] Area of curve MNBA \[=\int_{2}^{4}{\left( 1+\frac{8}{{{x}^{2}}} \right)}\,dx\] \[=\left[ x-\frac{8}{x} \right]_{2}^{4}=4\] ?(i) Area of curve ACDM \[=\int_{2}^{a}{\left( 1+\frac{8}{{{x}^{2}}} \right)dx}\] \[=\left[ x-\frac{8}{x} \right]_{2}^{a}=a-\frac{8}{a}-[2-4]\] \[=a-\frac{8}{a}+2\] ?(ii) From Eqs. (i) and (ii), we get \[a-\frac{8}{a}+2=\frac{1}{2}(4)\] \[\Rightarrow \] \[{{a}^{2}}-8=0\Rightarrow a=2\sqrt{2}\]You need to login to perform this action.
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