Paragraph: Consider the polynomial f ( x ) = 1 + 2 x + 3 x 2 + 4 x 3 . Let s be the sum of all distinct real roots of f ( x ) and let t = ∣ s ∣ . Question: The area bounded by the curve y = f ( x ) an

Question

Paragraph: Consider the polynomial f ( x ) = 1 + 2 x + 3 x 2 + 4 x 3 . Let s be the sum of all distinct real roots of f ( x ) and let t = ∣ s ∣ . Question: The area bounded by the curve y = f ( x ) and the lines x = 0 , y = 0 and x = t , lies in the interval

TestHub · Accepted Answer

∫ 0 1/2 ​ f ( x ) d x < ∫ 0 t ​ f ( x ) d x < ∫ 0 3/4 ​ f ( x ) d x Now, ∫ f ( x ) d x = ∫ ( 1 + 2 x + 3 x 2 + 4 x 3 ) d x = x + x 2 + x 3 + x 4 ⇒ ∫ 0 1/2 ​ f ( x ) d x = 16 15 ​ > 4 3 ​ ∫ 0 3/4 ​ f ( x ) d x = 256 530 ​ < 3 ​

Mathematics - Area Under Curves Question with Solution | TestHub

Options:

Doubts & Discussion