The area (in sq. unit) bounded by the curve 4 y 2 = x 2 ( 4 - x ) ( x - 2 ) is equal to

Step-by-step solution

4 y 2 = x 2 ( 4 - x ) ( x - 2 ) y = | x | 2 ( 4 - x ) ( x - 2 ) ⇒ y 1 = x 2 ( 4 - x ) ( x - 2 ) and y 2 = - x 2 ( 4 - x ) ( x - 2 ) D : x ∈ [ 2 , 4 ] Required Area = ∫ 2 4 y 1 - y 2 dx = ∫ 2 4 x ( 4 - x ) ( x - 2 ) dx       . . . 1 Applying ∫ a b f x d x = ∫ a b f a + b - x d x Area = ∫ 2 4 6 - x ( 4 - x ) ( x - 2 ) d x       . . . 2 ( 1 ) + ( 2 ) 2 A = 6 ∫ 2 4 ( 4 - x ) ( x - 2 ) d x A = 3 ∫ 2 4 1 - ( x - 3 ) 2 d x A = 3 · &#9