Let f : [ - 3 , 1 ] → R be given as f x = m i n ( x + 6 ) ,   x 2 , - 3 ≤ x ≤ 0 m a x x ,   x 2 , 0 ≤ x ≤ 1 . If the area bounded by y = f ( x ) and x -axis is A sq units, then the value of 6 A is equal to

Step-by-step solution

Given f : [ - 3 , 1 ] → R , f x = m i n ( x + 6 ) ,   x 2 , - 3 ≤ x ≤ 0 m a x x ,   x 2 ,   0 ≤ x ≤ 1 We have x + 6 = x 2 ⇒ x 2 - x - 6 = 0 ⇒ x - 3 x + 2 = 0 ⇒ x = 3   &   - 2 . Also, x = x 2 ⇒ x 2 - x = 0 ⇒ x x 3 2 - 1 = 0 ⇒ x = 0   &   x = 1 . Hence, the region bounded by f x is given by the following graph. Hence, the area bounded by y = f ( x ) and x -axis is A = ∫ - 3 - 2 ( x + 6 ) d x + ∫ -