First slide

Area of bounded Regions

Question

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

Moderate

Solution

$\int_{2}^{4} (1 + \frac{8}{x^{2}}) d x = 2 \int_{2}^{a} (1 + \frac{8}{x^{2}}) \Rightarrow {(x - \frac{8}{x})}_{2}^{4} = 2 {(x - \frac{8}{x})}_{2}^{a} \Rightarrow a = 2 \sqrt{2} = 2.82$

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