Let f x = x 3 + x 2 + x + 1 , then the area (in sq. units) bounded by y = f x , x = 0 , y = 0 and x = 1 is equal to

Step-by-step solution

f ' x = 3 x 2 + 2 x + 1 > 0   ∀ x ∈ R ⇒ f x is increasing ⇒ f 0 = 1 , so f x is positive in 0,1 Required area = ∫ 0 1 x 3 + x 2 + x + 1 d x = 1 4 + 1 3 + 1 2 + 1 = 25 12 sq . units