If the ordinate x - a divides the area bounded by the curve y -1-8- x 2- x - axis and the ordinates x -2- x -4 into two equal parts- then a -A- 2 -2B- -2C- 8D- 2

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Area between Two Curves

If the ordina...

Question

If the ordinate $x = a$ divides the area bounded by the curve $y = (1 + \frac{8}{x^{2}}),$ x - axis and the ordinates $x = 2, x = 4$ into two equal parts, then a =

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Solution

The correct option is B

Let the ordinate at $x = a$ divide the area into two equal parts

Area of $A M N B = \int_{2}^{4} (1 + \frac{8}{x^{2}}) d x = {[x - \frac{8}{x}]}_{2}^{4} = 4$
Area of $A C D M = \int_{2}^{a} (1 + \frac{8}{x^{2}}) d x = 2$
On solving, we get $a = \pm 2 \sqrt{2}$ ; Since a > 0 $\Rightarrow$ a = 2 $\sqrt{2}$

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