The area of the region bounded on the left by the curve y = |x3 – 1|, on the right by the straight line y = 12x

Engineering

Mathematics

Introduction to Area

Question

The area of the region bounded on the left by the curve y = |x³ – 1|, on the right by the straight line y = 12x – 17 and below by the x-axis, is

$\frac{9}{4}$

$\frac{7}{4}$

$\frac{17}{24}$

$\frac{13}{24}$

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x³ – 1 = 12x – 17

x³ – 12x + 16 = 0 ⇒ x = 2

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

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