A) \[\sqrt{2}\]
B) \[2\sqrt{2}\]
C) \[3\sqrt{2}\]
D) None of these
Correct Answer: B
Solution :
[b] The area bounded by the curve |
\[y=1+\frac{8}{{{x}^{2}}},\] x-axis and the ordinates \[x=2,x=4\]is |
\[=\int_{2}^{4}{ydx}\] |
\[=\int_{2}^{4}{\left( 1+\frac{8}{{{x}^{2}}} \right)dx}\] |
\[=\left[ x-\frac{8}{x} \right]_{2}^{4}=4\]. |
Since, \[x=a\] divides this area into two equal parts, |
\[\therefore \] Required area \[=2\int_{2}^{a}{y\,\,dx}\] |
\[\therefore \,\,\,\,\,\,\,4=2\int_{2}^{a}{\left( 1+\frac{8}{{{x}^{2}}} \right)dx}\] |
\[\Rightarrow 2=\left[ x-\frac{8}{x} \right]_{2}^{a}=\left( a-\frac{8}{a} \right)-(2-4)\] |
\[\Rightarrow {{a}^{2}}=8\therefore a=2\sqrt{2}\] |
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