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 _____ .

Step-by-step solution

Plotting the y = x x - 3 and x - axis between x = - 1 and x = 2 we get, Now area of the above region is given by A = ∫ - 1 0 3 x - x 2 d x + ∫ 0 2 3 x - x 2 d x ⇒ A = 3 × x 2 2 - x 3 3 - 1 0 + 3 × x 2 2 - x 3 3 0 2 ⇒ A = 11 6 + 10 3 = 11 + 20 6 = 31 6 Hence, the value of 12 A = 62