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JEE Previous Year Question

$Let A be the area bounded by the curve y = x (x - 3), the x -axis and the ordinates x = - 1 and x = 2. Then 12 A is equal to _______ .$

Topic: JEE PYQ

Answer: 62. Full step-by-step solution below.

Correct answer: 62

Solution

(62) A = \sum (x^{2} - 3 x) dx + \sum (3 x - x^{2}) dx \Rightarrow A = \frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} ()_{- 1}^{0} + \frac{3 x ^{2}}{2} - \frac{x ^{3}}{3} ()_{0}^{2} \Rightarrow A = \frac{11}{6} + \frac{10}{3} = \frac{31}{6} ∴ 12 A = 62

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