Area under the curveMedium

Question

The area of the region

$R = \left\{ (x,y):xy \leq 27,1 \leq y \leq x^{2} \right\}$ is equal to :

Options

A.$78\log_{e}3 - \frac{52}{3}$
B.$54\log_{e}3 - \frac{52}{3}$
C.$54\log_{e}3 - \frac{26}{3}$
D.$54\log_{e}3 + \frac{26}{3}$

Solution

Sol. [Key Concept: Split the area: $\int_{1}^{3}(x^{2} - 1)dx + \int_{3}^{27}(\frac{27}{x} - 1)dx$.]

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