Question

Let f(x) be a polynomial of degree three satisfying f(0)=0, f(1)=0. Also, 0 is a stationary point and f(x) does not have any extremum at x=0. Then the value of int fracf(x)x³-1dx is

• A. \( \dfrac{x^2}{2}+C \)
• B. \(x+C\)
• C. \( \dfrac{x^3}{6}+C \)
• D. None of these

Hint:

Use given roots and stationary points to construct the polynomial.

Answer 1

The Correct Option is B

Given conditions imply f(x)=x(x-1)². Thus, (f(x))/(x³-1)=1 ⟹ int (f(x))/(x³-1)dx=x+C