Area under the curveHard

Question

The area of the region

$R = \left\{ (x,y):xy \leq 8,1 \leq y \leq x^{2},x \geq 0 \right\}$ is

Options

A.

B.

C.

D.

Solution

$${A = \int_{1}^{2}\mspace{2mu}\left( x^{2} - 1 \right)dx + \int_{2}^{8}\mspace{2mu}\left( \frac{8}{x} - 1 \right)dx }{A = 8\log_{e}4 - \frac{14}{3} = 16\log_{e}2 - \frac{14}{3} }{= \frac{2}{3}\left( 24\log_{e}2 - 7 \right)}$$

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