Consider f x = minimum x + 2 , 4 - x , ∀ x ≤ 4 . If the area bounded by y = f x and the x -axis is 22 k square units, then the value of k is

Question

Consider f x = minimum x + 2 , 4 - x , ∀ x ≤ 4 . If the area bounded by y = f x and the x -axis is 22 k square units, then the value of k is,

MARKS App · Accepted Answer

Required area = ∫ 0 2 4 - y 2 - y - 2 d y = ∫ 0 2 6 - y 2 - y d y = 6 y - y 3 3 - y 2 2 0 2 = 12 - 8 3 - 2 = 22 3 sq. units