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Q.

The area of the region bounded on the left by the curve $y = |x^{3} - 1|$ , on the right by the straight line $y = 12 x - 17$ and below by the $x$ -axis, is

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a

$\frac{17}{24}$

b

$\frac{13}{24}$

c

$\frac{9}{4}$

d

$\frac{7}{4}$

answer is A.

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Detailed Solution

$x^{3} - 1 = 12 x - 17$

$x^{3} - 12 x + 16 = 0 \Rightarrow x = 2$

$∴ (2, 7)$ is the point lies on both the curves

$∴$ Required area $= \int_{1}^{2} (x^{3} - 1) d x - \frac{1}{2} \times 7 \times \frac{7}{12} = \frac{17}{24} .$

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