Question

Let \( f \) be a polynomial function such that \[ f(x^2+1)=x^4+5x^2+2,\quad \text{for all } x\in\mathbb{R}. \] Then \[ \int_0^3 f(x)\,dx \] is equal to:

• A. \( \dfrac{5}{3} \)
• B. \( \dfrac{27}{2} \)
• C. \( \dfrac{33}{2} \)
• D. \( \dfrac{41}{3} \)

Hint:

When a polynomial identity involves an expression like \( f(x^2+1) \), substitute \( t=x^2+1 \) to convert it into a standard polynomial comparison problem.

Answer 1

The Correct Option is B